If he won't tell you the trans code, then don't even consider having him fix it. Clutch pistons in 4t65e's don't really fail from what I've seen. You can have a seal that gets torn or that rolls out on the input clutch drum but that's not even that often.
Trans fluid might help some, but in all honesty it probably won't do much.
Trans additive usually is just a bandaid and can actually cause more damage/harm to the trans.
Recommendation
Go to another BIG trans shop and have them diagnose it. Tell them if they expect to make any money off you, that you want the trans codes to research what they say online. If they don't want to give you the code, then tell them it would be irresponsible on your part not to follow up. Come back here once you get the code and post it here.