Was payment specified in the Bid? If it's listed as payment upon completion, it's up to him to be a nice guy (and it sounds like you're screwed if that's the case)- at least as far as an early payment. If it's not spelled out, here's an idea...
Go over the job, and write out a description, point by point, while it's fresh in your mind.
List all the bid items, and time required for their completion. Location on the premises, materials used (including brand names), EVERYTHING.
List all the extras (and hopefully who/when authorized), and the time for their completion.
Get your supplier to write a statement if it was a distributor/supplier fault about the part. If it was ordered by your customer (wrongly), spell that out too.
Write a nice letter, explaining the status of the job, since there "appears to be a mild disagreement over the state of completion".
Mention that, due to the extras HE requested, if you were working a T&M job, he'd really owe you this much... "$X+"
But, you tell him, the bid is for "$X", as we agreed.
You're asking for "$Y" at this time, which represents % of X - tasks/time that can be proven to be accomplished that were in the original bid.
State your willingness and intent to complete the rest of the tasks listed in the bid at the earliest possible convenience.
Send it registered mail / return receipt. You may even want to send a copy to your permitting AHJ - some get real sticky about HO/contractor disputes.
Contact him (note date and time - cell bills ARE court admissible) and schedule your time needed to finish the original work if he doesn't contact you within 5 business days of his receiving your letter.
If he fails to pay upon completion, you have him by the nuts. Unfortunately, without written change orders, your "extras" could be argued by his attorney as "f*in around".. killing time that could have been used to complete the original scope of work. (even though it's not your fault, the argument could still be made - it's an american court after all)
Finish the original job. (quickly, but code-worthy) Then bill him.
If needed, then sue him.
As far as suing for a partially completed job? Hbiss used the magic word "default"... if you have completed 99% and then unilaterally call the job done, you still (legally) haven't complied with your contractual bargain, and you'll have to argue to be paid for the time you have put in.
Good luck.