My personal opinions only:

Use screws, no nails.

I occasionally get a crew who will still try to tack the board up with a few nails, then they screw it. I usually just have to shred and pull one sheet off the wall/ceiling with the claw of my hammer before they understand what I meant when I wrote in the contract "only screws" and "no nails".

I simply don't like nail pops. They can occur if the framing lumber shrinks and the lumber loses it's grip on the shank of the nail.

Other than that, I do prefer the first batch of mud be a setting compound. It's much more durable. The top coats can be drying compounds.

Level 5 is pretty much defined by what it is. I'd recommend you tell them that when they are done you, or your agent, will inspect the walls with a low raking light, and that the walls will be remediated to your satisfaction prior to final payment. A raking light really shows flaws, and with Level 5, you should have no flaws.

Good luck!

I've had good results with DensArmor Plus (Georgia Pacific). It's significantly heavier and harder than most paper faced drywall and requires skim coating.

Thanks Mongo and Ntruro. I will double check with the drywall folks. They were recommended by the carpenter that did my killer vanity for my soapstone sink, so I'm hoping they are top notch like Brett. They were very nice on the phone the 2 times I've called. They do small jobs and commercial jobs. The installer told me the cost of the fiberglass drywall was 2x the cost of conventional drywall. I told him to give me an estimate for both.8 j He did say that they would be using setting type JC with the last coat drying type JC. I didn't ask about nails verses screws, but I will when I talk to him tomorrow. I will also ask about tape, I read somewhere to not use paper tape for the fiberglass drywall, but to use synthetic.