Now I'm not a trem guy so take this with a grain of salt. I figure the agreement here is that "the guy" didn't install/replace correct springs to take enough tension and now the trem system is set so far one way as to make it so the tuners are backed out 100% thus practically useless.
First, this guy didn't properly setup your guitar. If you can, get him to refund your money or to do it right. Frankly, I'd want my money back but that's the last time I'd deal with him. It's in his best interest to do it right.
Secondly, the underlying issue thus far has been that the trem tension springs should be replaced. Have that done first as everything else is dependent upon that.
After that, you can think about continuing to setup the guitar.
Here is my check list for setups on my Les Pauls. A capo is used where ever fretting is needed just to free up my hands.
Once I've finished, I'll test everything but particular to pickup height, generally you don't want one pickup louder than the other. Since my pickups aren't identical, I usually have to lower one just slightly in order to make sure it's not louder than the other. For this, I just plug it in and listen, turn all knobs to 10, plug into my amp, and leave them for the duration of the test. Turn only the bridge pickup on, play a few chords and notes. Then do the same for only the neck pickup. (dont have the equipment to actually check how loud it is)
Nice work, but he has a fender with a tremolo....so some of this isn't relavant.