If you want to use a shotgun action you want to keep the pressures under 44,000 PSI for most useable actions, their are a few which will take higher pressures but even here you want a max load under 51,000 PSI NOT C.U.P.!! Check the pressures on the .375 flanged I am not sure where it falls.
The action you are looking for should have double underlugs and to be ideal have chopper lump barrels. You also will want a third fastner like a "Greener" cross bolt and it would be nice to have side clips on the barrel. Most actions will have the proof pressure marked on them some where and with basic math you will be able to figure if your cartridge falls within this pressure range. Also you want small diameter firing pins, lots of the old guns, and cheep guns have firing pin diameters that are far too large and even if the proof range is right bushing firing pins for a center fire rifle cartridge is a real pain. Good luck, have fun and be safe, and yes Brown's book is well worth the money.