They have been insanely helpful and nice, the entire time. What I'd love from you guys, is to let me know what you think I can ask for. They are offering a gift card to one of their nicer sister salons (Regis), but the amount is 'negotiable'. To make this relatively short, I'll just post pictures.
My hair before cut:

The example photo I brought to the salon:

Horrifying after shot, from the front:

Side view:

Second side view:

Back:

So, the gift card would cover a hair cut to even it out and some products, at the very least. But after doing a few searches online, apparently when a haircut is really bad, sometimes they will offer cuts/services for a few months until your hair is back to a decent state. I'm not looking for some insane amount, or anything silly like 'pain and suffering', but I do want to be fairly compensated. Advice?