I honestly don't think screenshots will work for missing FPs. I think you would just be out of luck and have to rebook. I never have lost an ADR. I just wing it with whatever is in the computer.
For the record, screen shots worked for messed up FPs for us ....
We had had an FP booked and then wanted to switch it because there was no wait, initially when you select to change the attraction for another, it shows up as if you were going to get the same time, it did not do this for us and gave us a time much later in the afternoon.
Took the screen shot to the kiosk of our original FPs and times, the CM tried to tell me nothing she could do about it, asked to talk to the special lady in the Guest Relations vest with the Ipad, CM told me "There is nothing she can do about it either" ... talked to guest relations, showed her the screen shot, explained what happened, were issues an Any time FP for that attraction.
This can actually be especially important because sometimes what system shows YOU, isn't what they see on their end.
For instance we were given another set of "Anytime FPs" on another day, which included ALL attractions, including wishes, Anna and Elsa ... etc.
We went to use them for wishes and were told they didn't cover wishes. She didn't show me her screen, but told me on her screen they weren't linked to Wishes, I showed her My screen where it did include wishes, and she let us in.