As soon as you drive the car, the gears will take a "set" and that's it.
A mile will do it.
Just accelerating one time. Not even hard.
This is why it is so important to get it right the First time. Otherwise, hell, we'd all be doing it ourselves, jockeying the gears around till we got them just right.
When you said that he was re-shimming and monkeying around, my first thought was,"oh ****".
If he did have the backlash wrong, the best that he'll be able to do is just move that sound around to a different speed or, maybe, it will be noisy while accelerating instead of decelerating..
I'm not there to hear it so, maybe the guy is right, maybe it's a bearing. Let's keep our fingers crossed.
I will say this though... A typical gear install does not go ANYTHING like this fiasco.
I feel for you buddy... I've been in this same situation.
$150, or whatever, worth of gears, is NOT worth doing anything stupid over.
Let it be one of those "life lessons"...