I do know that at least for humans, Cystine stones can sometimes be prevented by a high fluid intake. So you are on to something when you say you don't want to give him dry food.
It follows from that (just an idea of mine) that broths and soups made for him might encourage him to take on more fluid.
Now the point is -what with?
Fruit and vegetables are likely to help reduce stone formation.
This sort of diet leads to the formation of alkaline urine, which makes cystine more soluble and less likely to form stones.
Well, that's a guide for humans. A vegan diet is recommended. That means vegan sources of protein, not a completely protein-free diet.
However, some vegan sources of protein which are fine for humans are not suitable for dogs.
But for a dog...?
Well , dogs can certainly eat vegetables and some fruits in small portions, and gain a little bit of good nutrition from them.
So soups made with vegetables which are good for/safe for dogs would be at least helpful to give him some variety, on top of what you mentioned above
Carrots, broccoli, greens, turnips, potatoes, sweet potatoes, green beans, peas are all good vegetables tolerated well, and often very much enjoyed, by dogs.
Vegetables do contain a certain amount of protein (small amounts)
I also wonder about quinoa. That is technically a seed, not a grain, and does contain a good amount of protein. Dogs like it usually and it is fine for them.
There are other foods like buckwheat, wholewheat pasta, brown rice etc which could maybe be added to provide variety?
But I am unsure if those would be suitable or not. You could do some research ?
My advice though would be to have a consultation (remotely) either by phone, skype, facetime, or even email -with a veterinary nutritionist, and a "Holistic" one would be a good choice.
That might sound hard to accomplish, yet after researching, I did manage to find one (here in UK) whom I consulted years ago by phone (questions about my dog's nutritional needs for a home cooked fiet for early-stage renal failure.) The nutritionist was very friendly to talk to, and we had a thorough discussion.
Unfortunately I cannot remember her name, and this was in 2011.