Hello gtemkin,
I'm sorry to hear about your botched re-plaster job which I come across on many occasion, I am not all that shocked at the negligence however I am shocked that this has gone on for what looks like approximately 4 months now with no resolution. Leaving you with nothing but headaches and countless hours of wasted personal time I assume.
First of all I am in no way here to provide any legal advice, I am in the industry and quite familiar with negligence on behalf of Pool Builders and Contractors from personal experience in correcting such issues. It is my opinion that you are allowing this situation to get way out of hand when it is not necessary and it is my belief that you need go back to the root of this problem and end this once and for all.
After going through your post and trying to gather as much information as possible these are my findings, suggestions and solely my opinion. The problem is plain and simple a "negligent start-up technique" and you should have to look no further for a remedy period. Personally I do bicarb start-ups of some variation exclusively here in So. Cal. depending on the finish, temperature and fill water conditions. For the most part as Kim stated (if that's Kim)

with the exception of the words "properly done" being added so to say "a properly done bicarb start-up" would have eliminated any plaster dust from forming and not be an issue, but judging from your information that wouldn't have happened anyway, since they continue to muddle around.
Adding 'any" white powder directly to anything but a white plaster finish is beyond a rookie mistake and you can find hundreds of links stating that this should never be done, personally I don't even do this on white plaster. This alone tells me that the start-up person (I refuse to use "Tech" in this instance) obviously did not know what they were doing PERIOD! And the contractor is only dragging out the problem and inevitably making it more difficult for them to fix it in the long run as the plaster cures.
From the pictures you provided I looked at the first pic and thought HOLY COW WTF, then I realized you had highlighted the area :lol:, then after looking at the second pic it appears to me that the calcium sat on the bottom of the pool which is why it is darker in the center due to the plaster not needing to leech from this spot since it was saturated with calcium. The ring around the outside where the calcium stopped although prominent looks more uniform with the rest of the pool as far as color and pattern goes at least from what I can see anyway perhaps I'm mistaken. I have seen French Gray pools get brushed without using a brush vac which leaves a spot just like you have only white in color from plaster dust settling on the bottom of the bowl.
Your problem could be corrected within a 24 hour turnaround (depending on fill water pressure). The contractor is more worried about their bottom line which in turn gets hurt anyway in the long run as the longer they wait the harder or more difficult the work is to repair the problem.
ACID WASHING is 100% out of the question, it's a NEW plaster job whether a "re-plaster or new construction" it's still NEW plaster and the home owner should not have to degrade the surface by doing an acid wash because the contractor is a douche bag. What needs to be done is the pool needs to be drained and polished, which in many cases results in a phenomenal looking plaster job since the surface is smoother than troweling alone now.
24 hour turnaround is accomplished as follows:
Get two or three
"Trash Pumps" not submersible pumps make sure your water has been neutralized (for city legal purposes) and wherever you are dumping it can handle the massive volume headed it's way. The trash pump Home Depot shows in their rental literature can pump about 12k gallons per hour, with three pumps you could drain your pool in about 45 minutes for around $140. Polish (sand) the stain out first and then polish the entire pool and spa to a uniform color and when done fill it back up and do a modified bicarb start-up (filled pool non pretreated water version), plus 50 ppm borate added. I use perlite for filter media in D.E. and Quad D.E. filters, use whatever your comfortable with.
Make sure your bicarb and calcium are premixed and added through the skimmer, leave system running continuously until your water is stable as far as balancing goes, meaning there's no drastic pH changes any more.
Document everything you can recollect from how much or how little the start-up fool brushed the pool, to the chemical addition processes from day one in case you have to seek legal action. And from I have seen thus far the contractor doesn't have a leg to stand on, so don't give him one.
Long story short have them drain and polish it asap.
Good luck,
