You could set the bullet further back in the case. Lecac on youtube is the best Swiss K31 loader I know of.
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K31's are not rare around here. I would sell it of and buy another nice rifle. Good luck.
I ended up sending it off to JES and now it is a 35x55 "Swiss"
Rebored and rerifled, 3 grooves .357 with neck opend up.
Use 350 RemMag dies to reload.
Matches/exceeds 358 Winchester.
https://www.milsurps.com/images/impo.../3gWMSIZ-1.jpg
Barnes, Nosler, Speer
https://www.milsurps.com/images/impo.../ru6vBRq-1.jpg
It looks like you have re-invented the 9.3 x 55.
Anyone else?
7.5 Swiss and 6.5 x 55 share a common head diameter. (Give or take a couple of thou')
I recall reading somewhere, some-when, that there is a 9.3 x 55 SWEDISH round, used for Elk hunting. There is, of course, the 9.3 x 62, which is a functional equivalent of the 35 Wheal, and then some.
Anyone else considering this sort of adventure should check their local hunting laws to see if they have something against "military" calibres. Then, do some reading and then, if the barrel seems OK, do some tests with the rifle as is. and a selection of decent hunting bullets. You may be surprised.
Given a good barrel, the original cartridge is no slouch; pretty much in the .308 Win range, but given the faster rifling twist, and the larger-capacity case, capable of holding a bit more of the SLOWER powder of your choice to drive 180-190gn spitzer soft-points with gusto..
If it works, in the field, it's not a silly idea.
Have fun. Trophy pics by Christmas?