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Annoying, but salvageable.
https://rover.ebay.com/rover/0/0/0?mpre=https%3A%2F%2Fwww.ebay.co.uk%2Fulk%2Fitm%2F263851756171
[stupid link sharing convoluted hyperlink - sorry]
Buy that, which is 0.05mm. Cut a strip with some good sharp scissors, a little longer than the depth of the cup and just under one complete turn. Press the cups in with the shim.
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Annoying, but salvageable.
It's definitely salvageable but you know, buying a King headset and paying a shop to ream the headtube means this is not a job that @kjlem is looking to bodge.
Given the discrepancy in sizes of the cutters that are being sold as "1 1/8" reamers" I think finding out exactly what was used on the frame is a worthwhile step.
Might also be worthwhile checking the size of the cup with a couple different sets of calipers and/or micrometers. Like I said before, I expect quality control and tolerances at King to be pretty tight but you never know...
I tried and measured a few things. I took a Stronglight headset cup out of my mtb and tried it on the reamed Soma frame. I couldn't push it in by hand so atleast that is good sign.
I measured the Stronglight cup diameter and it is 34,1, I also measured the Chris king cup and that one is 34,0
When I dropped off my frame I told the bikeshop I was going to use a Chris king headset. According to the Chris king website headtubes should be reamed at 33,9 which means they reamed 0,1mm too much... It's not much... not sure what to do now, I feel temped to fit it with some bearing retainer and just start riding the bloody thing.