I must be missing something... why is your vet reluctant to flush the stones back into the bladder? That is normally a fairly routine procedure though sometimes the stones can be severely lodged in the urethra and it may take some forceful flushing.
And, 2, how does your vet know he would not survive a surgery? Heart murmurs rarely affect how a dog does during an anesthetic procedure, though it does make the whole process slightly more risky (I have done many hundreds of anesthetic procedures on dogs with severe heart murmurs and have yet to lose any... it is always nice having a cardiologist examine the dog prior to surgery to give the surgeon the 'OK' to proceed, but have yet had a single one say no to surgery).
And, 2, how does your vet know he would not survive a surgery? Heart murmurs rarely affect how a dog does during an anesthetic procedure, though it does make the whole process slightly more risky (I have done many hundreds of anesthetic procedures on dogs with severe heart murmurs and have yet to lose any... it is always nice having a cardiologist examine the dog prior to surgery to give the surgeon the 'OK' to proceed, but have yet had a single one say no to surgery).