Thanks for bringing home a senior dog and treating his heartworms!
Here's a long post I wrote about what to expect during HW treatment:
It wasn't clear from your post how long you've had this dog.
Are you waiting 3 mo. from starting prevention before doing HW treatment per the American HW Society guidelines? You can read the guidelines on their website -- it's very important to be sure you don't "miss" the juveniles that are too young to die from immiticide, but too old to die from prevention (the 3 mo. lets them "grow up" to the age when immiticide will get them, while the prevention keeps new babies from developing, so that all the worms are the age that immiticide targets, when you do treatment).
Also, it sounds like you just did the shots too. It takes several weeks to mount a full immune response after vaccinating. I would not do HW treatment during this window, as the immune system is "busy." The HW treatment is so hard on the dog that I would worry about it interfering with the immune response needed for the vaccine to work.
As for food...TOTW is a Diamond food, so it comes with all that baggage. Diamond foods works for a lot of dogs, but you must
keep lot codes on the bags and sign up for recall emails, given their history. If you want to feed it despite that history, Nature's Domain at Costco is pretty close and also a Diamond food, so you'd save some money. If the recalls with Diamond have you nervous, and you want to feed kibble, then you should look at brands like Fromm Four Star, Victor, and Champion (Acana/Orijen) -- independent companies that own their own plants, with a long-history of quality control and no major recalls. You'll likely have to go to a mom-and-pop dog supply store to find them. Victor sometimes can be found at feed stores, but mostly these brands support small, specialty businesses as their exclusive retail outlets -- and that is a good thing, as if your dog doesn't like it, those kind of stores generally take the food back and exchange it for something else to help you find what you want.
If you want to feed raw, I'd wait til he's through the HW treatment. His immune system is about to get walloped, and I worry about pathogens in immune-compromised dogs.
I'd really prefer getting his tummy sorted out before the HW treatment too. I would stabilize him on a food that works for a few weeks. Boost him with good probiotics (and ideally bovine colostrum). He should have been on 30 days of Doxycycline before treatment per the AHWS protocol, so THAT could be what's trashing his tummy.
I want my HW dogs as strong as they can be before treatment. It's always a hard call as to whether to do immiticide on senior dogs (they are sometimes candidates for a different treatment), but that's something you and your vet have to decide, based on the clinical signs of illness.