The description you are giving of the valve is....well....not really helping us.
Maybe you are talking about the governor assembly?
There are two lineups that go UP into the pump and there are many that go horizontal into the valvebody. There are two lineups that go into the auxillary valve body. Not real sure which ones you are talking about.
The TV valve way down in the valvebody is notorious for sticking (there are a few fixes for it) but don't know if that is the one you are talking about.
You are either overheating your transmission(valves will stick every time it gets overheated), or you've got a bunch of junk in your case, cooler, or TC and your breaking it loose at fluid changes and it's getting stuck in the valves. It's not like your engine. ANY junk in the tranny and a valve WILL get stuck.
$300 labor.....ouch. Most of the guys around here only charge $700 labor to rebuild the whole tranny(delivered on the bench).....why don't you take it somewhere else?
There are no valves in the case.
Before you take it to another shop, get some Lubegard, warm the tranny up, pour in the lubegard while its running and take the tranny out and cycle it through the problem area of driveability and see if it will break it loose.
George