Here's the list, as I make it out. The prime difficulty lies in differentiating the 6s and 8s I think.
NCC 1709
NCC 1631
NCC 1703
NCC 1672
NCC 1664
NCC 1697
NCC 1701
NCC 1719
NCC 1685
NCC 1700
But I'm pretty sure this is right at least based on the much clearer still, which seems to me more reliable at least at the moment until we have clearer scans. I'm very skeptical of the claim of NCC 1654, the third digit doesn't look like the 5 visible lower the the chart at all. I'm relatively convinced it's definitely a 6, and I think the other digits are 6s too simply because the only clear 8 seems to be a slightly wider character than the 6, with the 6 being distinctively more blocky.
This puts everything in the 1631-1719 number range which seems much more like a range you'd come up with if your intent is to put 1701 smack dab in the middle to me. Note also this implies there are 4-5 Starship\Constitution\Enterprise type ships under repair here, which is also consistent with the six reported in service at the time, in the episode previous to Court Martial. I think it's reasonable to assume the thought process was that these types of ships all had NCC 17XX numbers, especially when you consider any ship that appeared on screen was going to be the Enterprise model (so it's easier to live with the idea of the ships being in the 17XX series, and equally if they'd ever bothered with a redress it'd be an easy option. Really wish they'd given the USS Constellation the number NCC-1710!). IIRC Jeffries stated at one point his intent was that the Enterprise was the first of her kind by virtue of registry, design 17 number 01, but that's non cannon. Besides of which the viewers have only ever seen the USS Enterprise, NCC 1701 so it makes sense we're supposed to assume that NCC 1700, 1703, 1709, and 1719 probably look about the same.
Just my two credits.