It could be just about anything that she's not tolerating well so, cutting out the lunch meat is likely a great bet as a first step. Fingers crossed that it's the culprit!
If not...I hate to say this...but...it *MAY* be Purina in general. I had issues with Purina anything with Morrigan. More so, the Pro Plan canned foods but...every cat is different so, it might be just Morrigan.
If that doesn't work...try the Hills m/d. Its ingredient list reads like a bad novel, "corn, corn and more corn"...all broken down into "protein". Yeah, I know...but, it's the only food that she can safely eat. She's a kibble cat and nothing I tried worked other than to set off her colitis and vomiting. The ONLY food she could eat IS the Hills m/d so...go figure. But, what I can say is that anything was better than the bloody diarrehia, vomiting etc.. I had to up the dose to match the food and even now, it's not perfect by any means BUT...I'd much rather deal with a bit of extra insulin that seeing her so sickly and me...a nervous disaster, waiting to crash.
The other thing it could be, is...as you've said....she's hungry and she's wolfing the food down and vomiting it back up shortly afterwards. You'll know it's this if it's shortly after she's eaten. If it's HOURS later...not so much the idea of wolfing then. It might be an ingredient or something silly like the protein source. She might suddenly have developed an allergy to something in it like chicken or whatever. Perhaps, a novel protein like duck or lamb or venison or rabbit???
One last thing I can think of off hand....it might be that *IF* it is because she wolfs down the food...or...she has developed a form of regurgitation (meaning she takes very little effort to vomit it i.e.: no real wretching)...it could be an issue with her esophagus and sphincter muscle at the top of her stomach. Try putting her bowl on top of a few books or a shoe box. Try a plate instead of a bowl on something like books or a shoe box. Have you noticed her going right for her water bowl after eating? It could be also that she sucks up water like crazy and that will cause it all to come back up too.
I think it's going to take some experimenting to figure out what causes her to vomit like this but, you'll get to the bottom of it. She's certainly been checked out enough! OUCH on the wallet! But, at the least, you have some reassurance that it's not something obviously horrendously wrong for now.
As for your wife's inability to inject her...well...perhaps, she feels your wife's antsy or even reluctancy to shoot??? If your wife is impatient or just scared...it might be that YOU will have to be the one who gives her the shots and work it out with your schedule so that you can do it???? You and your wife need to talk that one out between the 2 of you, I think.
There's an answer, somewhere, somehow so, hang in there and keep trying BUT...remember....food changes too quickly....*CAN* cause
vomiting and loose stools right there. In this case...pick a food she likes to eat and try the removal of treats (for Morrigan, it was the freeze dried chicken pieces...Pure Bites, I think they were called), raising the bowls, small frequent meals (meaning no more than a tablespoon at a time but, given maybe, 6 or so times a day).
You'll figure out what works and what doesn't. it's all just guessing and experimenting right now. The fact that she WANTS to eat is a GOOD sign! Cats that have something terribly wrong...do NOT want to eat much.