Part of the mystery must be: What did the original maker use for brass, and what did he do for a chamber reamer?
In the 1920-1940 era, wildcatters had access to remaining supplies of many older and obsolete cases, and practically every one you can think of was wildcatted at some time. It is unlikely that a U.S. Krag would have been wildcatted for a European rimmed case, so the rifle was most likely intended to use some U.S. basic case. However, review of the dimensions of obsolete U.S. cases does not reveal any more likely candidate than the .405. Modern Hornady .405 brass (the samples I have) measures .461" at the base, and does have thicker rims than the typical Krag case, but I'd bet this was not always true of earlier production .405 brass, and, in any case, any wildcatter of that era (or this one) would have had no trouble thinning the rims, if necessary. When building rifles for rimmed cases today, I customarily survey the rim thickness of available brass and make the rim recess only deep enough to accommodate the average of those, with about .002" clearance, and adjust the rim thickness of thicker specimens if necessary.
As for the chamber dimensions: if the base of the chamber is as large as you report, there is no other common case which is really a better fit, though some real oddities like the .40-90 Sharps straight case come closer, and it is, of course, possible that that was the original base case. It is also possible (and not unlikely) that the reamer was made bigger than optimal at the chamber base, whatever brass was intended for it.
We'll probably never know - but keep us posted as you work-up loads, if you decide to shoot the rifle.
mhb - Mike