I have a .333 Jeffery and have wondered the same as you if I were to build one up.
I would go with a 1909 Argentine Mauser action to start and build it as close to a Jeffery or TypeA Mauser as possible.
One thing I would consider, though, (especially if I were planning on keeping the rifle to the end) is to barrel it for .338" bullets. A lot more shooting at a lower cost and greater bullet selection that way. Even then if it were to be passed along and the new owner tried .333s in it, it still wouldn't pose any problems other than accuracy. You could stamp the barrel under the wood to specify the .338" bullet too just to cover it.