Mr. Camp, I've been trying to work out the kinks in a BHP with an EFK standard, .357 Sig barrel. It works well until I put more than eight rounds in the Browning mags. Then the first two rounds nose dive and lodge against the end of the feed ramp. I gather this is a common problem with the .357 Sig BHP conversions unless the magazine feed lips are opened up. It's no where near as easy as dropping a .357 Sig barrel in Glock or Sig Sauer pistol.
I attempted surgery on a Mec-Gar magazine body and put a Browning follower and spring in it. It did improve feeding a bit--until I opened it up a bit too much. I lack finese with pliers.

I logged on here looking for a new course of action.
I wish I could get the combination up and running because the pistol groups far better with the new barrel than with it does with the .40 S&W. The 125-grain bullets shoot to the same point that I've regulated the sights to for 180-grain .40 S&W fodder. It doesn't recoil like the .40, but it will get your attention when fired between the outbuildings. It's not as bad as a .357 duty revolver but still way past supersonic.
I looked for a Bar-Sto or KKM barrel but came up dry. The EFK barrel locks up tight fore and aft, but it is a bit narrower than the .40 barrel. It moves from side to side at lock up as a result. The lugs show no evidence of rounding yet, and the chamber checks out fine with the headspace gauges I ordered from PTG.