Hi there! I adopted a standard poodle with allergies as well, which I just had the blood sent out this week for testing because I can't bear to see him suffer!
Did the vet go over with you how a hydrolyzed diet works? As a biologist, I can try to break it down a bit for you, but these allergies are FRUSTRATING!
So, proteins, are made up of 20 'building blocks', called amino acids. The term 'hydrolyze' literally means in the science world, to break apart. So, different proteins, like chicken, soy, beef, etc, etc, have different markers within how the 20 building blocks are assembled that make them each unique. When you add the 'chemicals' to break up the proteins into the 20 different building blocks, you are removing the dog's, or humans, or whatever's immune system's ability to 'identify' what it is that you fed them, so in theory, they wouldn't have an allergic reaction to it.
My question would be- is he still having allergic symptoms other than the stool changes throughout the day? It can take longer for a dog with established allergies GI tract to finish adjusting to a new food compared to a dog without allergies (so a typical dog could take a week, my Watson took 1 month for his stools to adjust!) So how long has he been on this particular food? I also saw the comment you made about not gaining weight- this can also be common in dogs with allergies, due to their GI system being 'out of whack' essentially.
Have you tried supplementing with omega oils of any kind (depending on her type of allergy symptoms this is common in allergy management & maintenance? I'd talk to your vet about how much to add to her diet. At first it will cause softer stools, but then it will normalize.
In regards to canned food, eating soft food only can be detrimental to your dog's teeth when eaten as the sole diet long-term (I'm not entirely sure the science behind it, but I'd imagine, the stress of crunching on things maintains their strengths). Depending on what type of labradoodle you have & the type of poodles that are in her DNA, the smaller the poodle, the worse their teeth can be, which has a genetic component, as do humans).
Purina Pro Plan- not all of their sensitive skin & stomach lines have chicken in it, I am unsure though about the entire list you gave, but it is mid-line price wise (about 1/2 of a hydrolyzed diet though!), vet recommended, and a high quality food without "meat meal". I found that it is difficult to find a kibble that is NOT grain free (a hot topic in & of itself, but my vet does recommend foods with grain in it, but is also limited ingredient). Granted, depending on the allergies, the quality of life vs. length of life.
