However, I do accept that its hard to run a centralised state like 18th century Britain with the thirteen colonies attached. So I'd say, give the colonies a measure of autonomy, but in return less representatives in Parliament. That autonomy also wins them less taxes from the British Parliament, and an ability to raise their own colonial taxes and a right to spend those taxes however they like. I think a Secretary of State for the American Provinces would be useful too.
I agree with this part. I think if we look at what both sides did, we can find a workable solution that both sides can live with. Something along the line.
1) I think we get some symbolic representation in the House of Lords for the bigger colonies. There are a couple of good ways to do this one. One the Queen/Parliament can persuade existing lords to move to the Colonies and become established in the colonies. They can be given large land grants or upgraded titles or upgrade orders of Knighthood. This option should be 100% acceptable to the other Lords. Or we could just start appointing new American Lords and require them to live in America. Say 2-3 Lords to begin and maybe one per decade. They can also be required to maintain some standing forces or raise some revenue. So for example, the Lord of West Point required to maintain a fort and 2 companies of Red Coats makes sense. And there are American families rich enough to do this type of action. After all, we have Irish and Scottish Lords, so why would this be such a big deal? And you will need some provision so the Lords appointed representative (say his son or other blood relative) can go to England to vote for the American Lord.
2) The UK was not trying to impose full tax on the American Colonies - seems like 1/3 to 1/2 UK levels. The UK does not want to give the Colonies 28% of the vote. This begs for a compromise where the colonies get say 1/3 the votes they should for 1/3 the taxes. It also provides an out if either the UK needs a lot more tax revenue or the colonist greatly desire more representatives. Exempting Puerto Rico from many USA taxes has gone a long way towards them not asking for statehood for over 100 years. Same idea. The MP are probably selected by the state legislatures.
3) Under the USA system, we were much more comfortable imposing duties on states than taxes. There is a potential compromise where the colonies can "win" on lower taxes and representation, but the UK can require the colonies to maintain a standing army that a portion can be used throughout the empire.
IMO, it was a solvable problem if there is a desire to find a solution. The details could vary widely, and perhaps each colony has a different deal with the Crown, but it could have been prevented.