He wants to see Skyrim become self-determined. Being imprisoned and executed kind of interferes with that.
But he is a coward anyway, he ran and hid like a child frightened by shadows in the night before arriving in windhelm and claiming what he did was honorable, if he was captured and executed he would've became a martyr among those that believed in his cause which would further fuel the civil war.
If Elisif is claiming that Ulfric used a Thu'um that in and of itself caused Torygg to be dismembered, i.e. shouted to pieces, then she is either lying about what she saw or was so disturbed by the outcome that she is unable to remember the incident clearly or else she never saw what happened in the first place. I am sympathetic enough to her grief to assume that the second possibility is the most likely. However any claims made by her or anyone that Ulfric literally shouted another human being into pieces cannot be taken seriously as an accurate report of what happened, because as I've already stated Ulfric does not know a shout that does that, the end.
The only people who actually say this are the guards so its more likely that it was a rumor, Elisif never actually claimed he shouted Torygg to peices only that he used his Thu'um which in itself should be considered a act of defilement of the teachings of Kyne thus making Ulfric a heretic towards the divines.
Sure, Igmund made the deal, but he had Imperial support in the matter. It lay in their interests to quash the rebellion, and they got it free, since they were able to turn on Ulfric and his militia afterwards. Pretty good deal for them. Right up until Ulfric killed their puppet and declared open war on them.
No, no he didn't have Imperial support, no where in any bits of lore was that confirmed also if Torygg was a puppet why did he agree that skyrim should be independent? That doesn't sound like something a puppet king would say, Torygg agreed with Ulfric but he said that now is not the time for it, why? Because you have a sleeping beast that still threatens all of humanity.