I'm not sure that concessions to Parliament would have done anything but embolden the radicals. In much the same way, concessions to Islamic radicals do nothing but embolden them to seek more concessions and eventually the heads of the infidels. They are not interested in negotiations, only power.
The Levellers and Fifth Monarchy Men were already seeking to overthrow the monarchy and the peerage and set in place a religious government (run of course by them). But the majority in Parliament (probably horrified when they realized what they had done) asked Cromwell to be king. He had the good sense to refuse the title, but ran the country as a de facto king. (He also severely quashed and executed the radicals, as Charles had failed to do.) His son Richard inherited the job of Lord Protector (showing that it was a de facto monarchy) but couldn't manage it, hence the Restoration.
Cromwell's body wasn't torn limb from limb, he was beheaded post mortem, the body thrown into a quicklime pit and the head displayed at Westminster until somebody stole it. It was eventually buried at his old college in Cambridge.
Wrt the American Revolution, the problem wasn't George III, bless his dim little head, but Parliament. Monetary exploitation of colonies without representation almost always leads to difficulties once the colonists realize they are being had.
I wouldn't have stood with the radical republicans like Sam Adams and his ilk. THOSE are the kind of folks who bring you the French Revolution . . . and Sam would have done something of the kind if his cousin John and other cooler heads had not prevailed (Sam was instrumental in precipitating the Boston Massacre, and it was after that that he was shuffled off to a quiet job out of the mainstream.)
Under the circumstances, I would have stood with the Virginians and Georgians (including my collateral ancestor George Walton) who reluctantly severed ties with Britain.
FReegards!