Ok..maybe a 307 isn't a big bore but it is housed in a variant of the Big Bore 94 so I will post this here. I just bought a Winchester 94 in 307 from Ontario and it should be in the Yukon by Valentines day. Now finding brass and ammo is a bit tricky.

Looks like the 308 Marlin express is a similar case, same rim,same base dimensions but a bit shorter in OAL and shoulder placement.

So I ordered a box of 308 Marlin Express brass and will try annealing the neck, then necking up to 358 caliber to create a false shoulder when I run them back through a 308 die. This will hold head space. Fireformed they should create a perfectly acceptable 307 case but a bit short necked and in overall length.
Given you often need to shorten a case by 1/10th of an inch to use flex tips anyway it shouldn't really matter at all.

I'll let you know how it goes. A 160 grain Flex Tip at 2500fps and a 2.5X leupold ought to make a nice little package for myself, my wife, and my two left handed children. Nice companion to our 348 and 405 that will be more family friendly.