Grant, I would consider doing an echocardiogram before you start SubQs. He has a heart murmur which means he could have serious heart issues and SubQs will throw him into heart failure if that is the case. I went through this with Ophelia. We ID'd heart issues almost simultaneously with the kidney issues due to her heart murmur (echocardiogram every 6 months...). I could not do IVs or SubQs.
You can also syringe water into him, too - and that will not hurt his heart. For instance, 15ml of water equals one tablespoon. If you syringe 15 ml per hour (which would equal 15 tiny squirts of 1 ml each - maybe two minutes to accomplish, tops) you can do that 6 times per day and it will equal 90ml of water which is pretty good. It will mean setting the timer each AM and PM to do it once an hour, three times AM and 3 times PM. IE 630 AM, 730 AM, 830 AM - and again at night. Safer than the SubQs.
Ps. unsteadiness could be dehydration, or it could be potassium. Have they mentioned TumilK? I would ask for another blood check to see where his potassium is.
I'm sorry you are going through this. Poor kitty.