I realize there is no good reason to do it,as many other cartridges as are out there,but,IMO,starting with 8x57 brass,necking it up slightly to use .338 bullets,210's or 225's,and maybe even Ackley improving it seems like a good Mauser cartridge.
I do not know if Hornady is still making the brass,but the Col Cooper's 376 Steyr was made to fit in Mauser length boxes,and,IIRC,its a fat case with a rebated rim.Might have potential.
Another option might be the Dakotas.....300 and .338.Instead of short mag or the extra long Ultra Mag,think a 30-06 length Ultra Mag fat case with a rebated rim.
A lot of work and $ but if you just have to have a crazy project,enjoy!
Before the non-belted options came along,I made a .375 Chatfield-Taylor,aka 375-338 in a old FN Supreme magnum action.I neck down 458's.
A mild pressure,accurate load gets me 2600 fps with a 260 gr Accubond or a 270 gr Speer using Re-15.I'm sure more could be had with 4350 or Re-17.The .416 Taylor is one step larger bore.Both of these are a standard wildcat,which helps with dies and reamers.
Oh,Wyo,I get adding the 3rd lug as a strength thing.Maybe.I think the original design intent of the third safety lug was if you had the initial lug failure,things were really bad!The case could fail and release the pressure.At least then the pressure would not continue to spike.The third lug was there to arrest the bolt from entering your head about at the cheekbone and blowing out the back of your skull behind the ear.Sort of a contingency plan.Just another way to approach it.
I used to bust tires.Sometimes that meant going out on the road to work on semi's.I had a gasoline powered compressor on my service truck to drive my 1 in drive impact wrench.Sometimes,that 1 in gun would not loosen the lugs.My field expedient solution was to hold down the safety pop-off valve of the compressor tank down and run the pressure up.K-W Knock-er-Loose on the threads,more Marvel Mystery oil in the gun...Got the wheels off,I'm still here....seemed like a good idea at the time...
"Scotty,keep those shields up and give me another warp!"
"But Captain,the dilithium crystals are glowing red and I'm afraid she's going to blow"
"Just 30 seconds Scotty"
"Aye,Captain"
Hmmm.The 375 Ruger Compact Magnum necked up to .404 or .416?