Fourintune of Cedarburg, Wis., specializes in restoring cars made across the big pond. The shop is most famous for its work on Austin-Healeys, but has also restored several Jaguars, Aston Martins, Rolls-Royces and Bentleys. Fourintune has finished several cars with special historical significance - like the Austin-Healey 100S once owned by famed child actor Jackie [...] https://www.hagerty.com/media/archived/tips-from-a-british-restoration-shop-2/
The "allowance" notion vs. firm quoted budget is important to understand. Your engine is supposed to be a standard rebuild and they open it up and something unexpected isn't good. New part is pricey and/or hard to find.
The other aspect is the changing of the scope of the project mid-stream. Many shops love this upsell. How many Hot Rod Magazine articles start with "I was just going to do a driver, but then we got it all apart and..."
It is important to document restorations and or modifications. This is you document to the quality of the work, parts and who did the work.
Too many cars and trucks are half a$$ed and often do not realize the value they hold due to lack of documents covering the money and time spent in a quality job being done. Get a note book and put in the receipts and photos of all stages and steps along with who did the work.
Also do everyone a favor. If you are going to commit to a restoration go all the way and commit. Backing out or trying to go cheap once it is started does no one any good.
It prevents the shop from doing it right or at all. It also prevents you from having the vehicles as you want it. If unsure of being able to affording the job best to wait till you know for sure.