Okay, time for my own dose of blasphemy, but with more of an AR spin. I kind of want to try this someday, even though it's a ridiculously expensive build.
For the lower receiver, an ARES Herring:

For the upper receiver, an American Spirit Arms side-charging 24" varmint upper.

And a close-up of that receiver, thumbnailed:

And, to double the heresy,
plug the gas tube at the block. This makes a left-hand-charging, straight-pull bolt-action AR with a Monte Carlo stock. Slap on a good bipod and scope, and this thing would be an outrageously accurate rifle, even at extreme distances.
And if I'm feeling really heretical, I'll put wood furniture on it. I hear the Herring takes an 870 stock, so it shouldn't be hard. At the very least I'll get a synthetic with a higher comb, because seriously, that stock is WAY too low.