I hope this message finds you well, present circumstances excluded. In similar situations like this in the past, I have found success by taking the following course of action:
(1) Send the jeweler a certified letter with a return receipt in which you inform him that the work was still not completed satisfactorily, and that you are going to send the ring to another comparable jeweler in your immediate vicinity to have the work done correctly. Tell him that you are going to send him the invoice for the work to be completed unless he, within 7 business days from the date of the letter, sends you a full refund for all work that he has completed and that you have paid for. Tell him in the letter, if you do not hear from him in that period of time, you are going to take that as an acceptance of your demand and a willingness to pay for the work, or reimburse you for the work that will have to be completed by someone else.
(2) For your protection in appearing reasonable, I would get written quotes for the work to be completed from three jewelers in your area. Keep those quotes and probably attempt to use the middle priced quote for the work.
(3) Invoice him for the work that was completed to fix his mistakes. With the invoice, tell send a letter (once again certified with a return receipt) that states he has 30 days to pay the invoice or you intend to take him to court over the issue to receive reimbursement.
(4) If he does not reimburse you, then you may have to take him to court. You may be able to use small claims court, dependent on the amount sought for reimbursement. Unfortunately, unless he comes to Connecticut to do business, or unless he advertises in your state, you may have to go to Maine for court.
Documentation and your appearance at being reasonable will be the key to winning in court and getting made whole as a result of his incompetence. This is why all correspondence should be via certified mail with return receipts. Obviously, make copies of all letters sent as well. This will be your evidence in court...if things progress to that point.
Like I stated before, I have used this method successfully mainly times before, on both large and small amounts in question. I feel certain it will benefit you as well. The jeweler really has no leg to stand on as a means of defense.
Let me know if you have any other questions or comments.
Best wishes going forward.