Well I can't sleep so here are my unfocused ideas (which should serve as a basis for conversation, not arguement or anger

).
Because I'm negative I'll only say the bad things or different things. Everything I don't mention (unit fluff text, use of 1st ed plastics etc etc) assume it is brilliant

Before going any further believe it or not (and many don't) 15 activation sieger arty armies are balanced (I tend to 14 activations now when going popcorn), even when they weren't the best tourny players had pretty much figured out how to beat it and I haven't lost to siegers in absolute ages now. Indeed a handfull of times I have been a few stands off anhililating them (with chaos hordes and marine drop armies admittedly but you get the point). Its largely because unlike other popcorn forces yours die with incredible speed when (slowly) attacking and if the strategy is entirely defensive all you can do is draw. In fact lower activation ragnarock armies are often harder to beat, not only because its not expected but all those garrisoned tanks in emplacements can be chilling!
First off - unit names. I prefer the Imperial Guard/Planetary Defence force label, followed by pattern name like teh rulebook (though you can differ). Really if a model is identical to the Siegers it shouldn't get any new name.
Rapiers. People say not as nifty as thudd guns. I disagree as this list has even less infantry AT than the siegers and the idea of giving every company 3 rapiers is a necessary one.
Otherwise before going deeper. Your list (well we know it started off as mine

but you get blamed now) is of course a sieger varient made to fulfil my craving not to use nice new models and as I said elsewhere that was fine for your original 'simple' supplement but now its a lot grander and they are somewhat wanting in comparison to your high standards elsewhere.
So various changes have been trotted out as ideas and I think you had a tighter timetable than you do now. So perhaps open to a few changes? If they look thought out they are are unsurprisingly mostly cut and paste from some brainstorming and early testing notes when I was playing with my directors cut list (gods, back in the day three clubs to choose from to play Epic and in different country to family, which of course has many negative points in addition to this one good one!) before I got lazy and went for a de skilling rather than a serious change. Note these ain't mostly been tested and when they were it was part of a very different army.
List structure. Since you have gone for the 1 core 3 support and have such an awful core I think you could do with a few changes.
First off special rules
BTS - lose the must take one and instead on the army list make it 1 instead of 0-1. Keep it as the sole BTS though as its different.
Fortified positions - just make them a support formation pick, lose the sieger 1 per company restriction (these guys have been preping for a while and it shows the choice of where you put resources)
Special rules/Units/list
Iterators
I see a lot of discussion on this chap. Either stick with what you've got (effectively every formation in the army gets one) or... do something a bit different. The infantry are pants so give them a boost. Scrap the special rule, change the unit and stick it only with infantry.
In essence becomes Infantry, move 15cm, save 6+, CC4+, FF5+, CC+1 (no need for MW), give him something like a plasma gun then Leader and Inspiring
Plus points are many, not least they stop looking so much like a commissar equivalent from the outset. I would even consider giving them back fearless to show how hard it is to stamp out heresy

Units
Fortifications
Replace barbed wire with minefields (dangerous terrain test to any unit passing over, infantry, tank, skimmer). Easier to make, bit different.
Snipers
Lose scout. They are there as a formation option. Lot better as normal chaps as they can still garrison and look like pdf versions of the emperors best (the regular guard and any krieg snipers you may have).
Siegfried
I suggest a different name.
PDF bomber and figher
Not tempted to use 2nd edition models? Shame the bombers armour is so good

Infantry
I'm happy they are the worst of the worst (they could turn to chaos and get AP6+/AT6+ if they get desperate).
Sappers
Surely FF IC on the heavy flamer?
List
Go with the idea for bigger formations. Currently it is just cruelty to pay that much for stuff that poor. The siegers are 1 autocannon and 9 stubbers for 175, you are 5 stubbers for 200 (that loss of 45cm shot is very big deal in my opinion). Easiest thing is to add on the infantry upgrade so
Core
1 Regimental HQ - SC, 15 Infantry, 3 rapiers, 1 iterator - 350
1+ Infantry Company - HQ, 15 Infantry, 1 iterator - 225/250
Or
1+ Infantry Company - HQ, 15 Infantry, 3 rapiers, 1 iterator - 300
Have a little bit of background talking about rapier production and impact of krieg armour.
Upgrades
Mortars
Are you sure those mortars are 75? I found them dead handy and couldn't put them lower than a 100. Then again if you are limiting inspiring and leader in a big way they should get something!
Rough riders
Remove, make into company of ten in support section.
Support
Rough rider company
Bring in as company of ten strong chaps for 200 (remember no fearless or inspiring for them, and only one attack).
Add in fortifications with minefield change (still 100 points). Have two options for swaps, so you have an entry saying 500mm of minefields, 500mm of trenches or 6 emplacements and up to 6 bunkers or emplacments (or any mix of the two as long as its 6). So if you wish to emplace vehicles in a big way you can more easily, also making things a bit different.
Engineers
Lose the split up rule. Removes a bit of faqing and confusion and makes them more scarce. Actually I would remove the 0-1 restriction as they are overpriced (but very useful to have) so self limiting. Maybe consider adding the option of 2 sappers for 50 points as a new upgrade option.
Snipers
Since they are losing sniper would have to come down in price probably or go up in numbers (I favour the latter but the former is alright if you want a 100-125 point formation)
Heavy Tanks
I would strongly consider making it a 9 strong company for 425.
AA
Might want to consider swapping for those FW things, but its a very minor point if you do these other changes.
Stormhammer
As its fairly pants and can't be fearless maybe make it 150/175? (Probably worth 150, unless you use masses of them to support assaults when worth 175.) Or be a bit radical and have him garrison to fit the loverly fluff above?
Firestrike
Lose the gun emplacements. Its a harsh world, if you want them why do you think you can swap bunkers for them?
PDF fighter
4 for 200 seems a bit much, you could bring it down to 175 for 4 considering they are so sub par for ground attack and on the same point per AA hit as thunderbolts (75 points per hit on intercept).
PDF bomber
3 for 250
And lastly, those are 1st edition infantry, not second

(in the model guide bit - I made my 1st edition guys into a very interesting jord whatever force, with infantry carrying lascannon instead of autocannon, tis neat but half done).
Backstory
I've said before what I think about chaos but how about instead of being shot the Mos SC goes on to infamy as the head of a penal regiment, dying on some chaff mission?

Of course if you really want
three new armies to satisfy hungry gamers I suggest a background re-write and sticking Salamanders in instead of White Scars

- nothing says dead seige troops more than Multi Melta and Heavy flamers (and its 98% done, just have to sort out redeemer and maybe drop a couple of units like helios if things look too complex/crowded, plus between us me and BL have some fantastic models all painted - you've seen the sallies I mostly got off PG?) and of course they aren't in the EpicUk book, making them even more unique! Course that's
a lot of work and they are vaguely penciled in to a future supplement idea.
So overall bigger formations a few tweaks to make it more different and the loss of a lot of fearless and leader. Maybe too much harsh but who knows. The rag company might need a command tank with leader perhaps. Super heavies that aren't fearless is a big departure from the guard as well. Overall I would expect 10 activations to be the practical amount aimed for. Biggest worry is with the loss of the activation crutch combined with so little leader the army grinds to a halt.