but given that so much of a good custom shirt is down to the person doing the measuring, I'm not convinced a remake is going to do me much good.
I agree with the measurements part. Do you have another OTR or MTM shirt that you want duplicated? Use that.
I provided my own measurements based on another shirt. The first came in tighter than I would have liked, so they remade it per my updated measurements. The fit on the remake is near perfect.