Looking at the pics I'd guess that the core support could easily be straightened. You'll need to pull the radiator because tweeking the core support could damage the rad in the process. Rent a portapower (or buy one at HF) and push it back. Remember, little of that shows and it doesn't have to be perfect to do it's job properly.

If the collider (isn't that the person who hit you in a collision?) is paying - well, turn it over to the body shop and let them handle it! Few body shops fix anything anymore as it's simply cheaper for them to replace panels - and they're not buying the parts. That doesn't mean it's better to replace.

Having a frame shop pull the front back in shape is a great idea, too, and well worth the expense.

Just so you know where I'm coming from, I've been doing body work for about 50 years though not generally as a profession. I've done a TON of it and have earned extra money by putting repairable totals back together with good success. I have some formal training in the field. So I do have some idea of what I'm saying. Take a look at my build thread and you can see the last few pages are the body work on my OM617/S-10 project.

Dan