OMM is on point with all his information.
I have an open dialogue with Muscle Car Restorations in Chippewa Falls, Wisconsin. Mostly before the pandemic and I recently got caught up in elder care for my folks. They have done several a bodies and you may have seen their restoration articles in Hot Rod and other car magazines.
Upon your first contact with them, they are looking for a high end build with a blank check. Keep in contact with them and show them you don’t have deep pockets and are not an easy mark. They have an open house every year, I go. I visit with them at car shows. They have a calendar of upcoming events on their website. I talk them up to prospective clients at their car shows, they have shook my hand and thanked me. Its all about getting to know them and making sure they know you. Then you can get down to hard negotiations. Tell them exactly what you want and how much you are willing to pay, you will be low and they will be high. Make sure they understand what they have to gain by working within your budget. An outstanding restoration that is word of mouth broadcast by you as to who did it is the best form of advertisement. Pass out their business cards, show them what you can do for them.
Keep in mind that high end restoration shops have a waiting list and figures into a 9 year restoration.