Since you're on a retirement extension, there's no need to go get anything cancelled - immigration at Chamchuri will do that when they put the LTR in your passport. Congratulations!
As a UK citizen, you can get a 60 month E2 visa on the basis of reciprocity. Since your wife is Thai, she can only get a six month visa - see the reciprocity table below. As noted elsewhere in the comments, this only affects when she can enter the US, not how long she can stay there.
You only need a police report if you're trying to replace a passport that was lost or stolen. If you can submit the passport - which it sounds like you can - then there's no need.
Correct, all overseas passport applications automatically get the large book (but it's always worth checking that box anyway, just to be sure). And Laos does have an e-visa, but unfortunately it's not for every purpose and can only be used at a select few entry points 😞
It applies to every country. An embassy or consulate can print an emergency passport (12 pages, valid for one year), but all regular passports have been printed in the US for many years now.
All an agent can do is take the documents that you provide and submit them by mail exactly as you would have done. They cannot change or speed up the process.
There is no way to "streamline" the process, and there is no expediting option overseas. Just go to the embassy website and follow the instructions exactly, and you should have your new passport delivered to your door in about 3-6 weeks. The process will not be any faster in Vietnam, because the bulk of the time is the wait for the new passport to be printed in the US and sent back to the embassy.