Tony is right. There are 2 or 3 types of stones, some can be controlled with diet, some not.
It sounds like they are too large now, but they can sometimes be washed out by irrigation with the dog under sedation. Unfortunately, the only other option would be surgery. They may or may not recur.
A major concern is they will cause a blockage and the dog can't urinate, this is, obviously, an emergency situation.
I don't understand why you would want to try to put him in another home due to his health issues and his anxiety issues. Not sure where you rescued him from but you have had him for a while so doubt the rescue would be much help but you can try contacting them perhaps.
Many of us know the financial burdens Vet bills can be and doubt anyone here is judge mental to your circumstances. You have obviously put a lot of time and effort into this little dog and bless you for that.
As difficult as the decision to let him go, would be, you might have to make that decision when it comes down to a quality of life issue. That can often be the last act of live we can do.
Wish I had better answers and maybe someone else will.
Good luck and this little dog has been lucky to have ended up in such a living home.
Please do update.
Calcium oxalate bladder stones cannot be dissolved using diet - but a change in diet can certainly prevent them reoccurring once the stones are removed. The stones form due to excessive calcium. This can be caused by diet, but unlikely, and is much more likely to be genetic, particularly in Shi Tzus. Some medications can also cause stones of this type, particularly Prednisone and Furosemide.
Surgery is really the only certain way of treating the stones, though Lithotripsy is another possibility. This is where a laser is used to break the stones up into small enough pieces to pass through the urinary tract. Lithotripsy is less-invasive than surgery, but also less certain to succeed, and potentially just as costly (worth asking about though, just in case).
Hope this helps.
Tony