Under the current rules, there are no towed Heavy Artillery. At least, none that I can think of. The closest thing would be the Earthshaker Platform as used by the Planetary Defense Force list. Based on the time-scale of this game, I think that your proposed restrictions are a bit much. Assuming any Heavy Artillery are ever statted up that would require being towed, it would probably be simpler just to give them two Special Rules. The first would be to say that it can be Towed as per a Light Artillery. The second would be to give it the existing "Move or Fire" restriction.
Most of the models you listed are Light Artillery, except the Ork Traktor Kannon. That is listed as Heavy Artillery, and has it's own Move value. Thus yes, the "Heavy Mortar Bundle 01" as pictured, should be Light Artillery, as is the Thudd Gun. Note also that making the Thudd Gun Light Artillery was GW's idea, not mine, so don't blame me...

The Frateris Militia do have the "Infantry Gun" which is basically what he is trying to do with his "artillery carriage" rules. It is classed as Light Artillery. See the "adeptusministorum.pdf" page 13 for the picture. Actually, that is a good point. Since that frame already exists in the current rules and acts as normal Light Artillery, the special rules for "artillery carriage" are not necessary.
On that note, there is already rules for the Centaur, even though it does not use that name. See the "Artillery Tractor" in the "adeptusmilitaris.pdf" page 15.
Thanks for the image of the Cyclops. That is a heck of a lot larger than "a briefcase with tracks" as was described earlier. There is no way that could be classified as Infantry under NetEpic Gold rules, as it is clearly larger than a Rapier or a Tarantula. It could perhaps have a Special Rule allowing it to fit inside a Chimera, but it would have to count as the entire capacity (IE, as two stands) to do so. In my opinion anyway. Thus it should probably be considered to be Walker for Pinning Class and Vehicle for Terrain Access.