brifters, or just brakes....I don't have brifters, So I wouldn't know about those, but assuming they work the way almost all brake levers attach, you shouldn't have any problem with just tightening the screws a bit more till it is tight. the clamps will form around the bar into the new diameter. They need to be able to because a lot of drop bars don't stay perfectly circular when the curve. If you want to put them back onto a 23.4 mm, you will have to widen the clamp with pliers or something similar until it will fit again.
The only levers I can think of that would work off hand would be the ones that come on the old GMC Denali bikes or other rebranded kent road bikes, they had a steel two-piece bar on those bikes so they could use grip-shifters and they came with some crappy aero levers that had appropriate clamps, I've worked on a few at the co-op. The other idea is finding a pair of vintage city brake levers like these ones and poaching the clamps to use with whatever levers you can.
go for the shims under the brake levers you get, and like.
23.8 - 22.2=1.6/2=0.8.
Shims would be of 0.8mm thickness.
Mittelmeyer (D) makes a shifter for Rohloff hubs, that is a bigger size, center.
and so will go around the curves of a drop bar. the clamp is an eccentric
piece with a slot for brake cables to pass thru.
a regular Rohloff shifter won't do that , so Brake cable will be in the way.
older style Cable out the top Brake levers will be fine,
Aero type you need a cable routing that will be away from that shifting
grip so as to not interfere with your hand , shifting..
This place is faster, it also has to be something I can get locally. If it isn't a standard part because of something like "didn't you know all Keirin track bikes are that size", Then I will just go with the shims.
Well, I didn't mean for you to buy from Thorn necessarily. I just thought that sending them an email explain to them that you bought that bar from them and if they knew of any levers that would work. It might not be a special brake and that a common lever might work.