help me get shot of my confusion

I was in a meeting earlier (can't tell you what about - top secret) and someone used the phrase "get shut of" with its usual meaning of "get rid of". This always sounds jarring to me, because I say "get shot of" in that context, and I've always arrogantly assumed that that's the correct usage and that "get shut of" is based on a mis-hearing of the phrase.

It occurs to me that I've no basis for that view other than a blithe assumption of my own rightness, though, which is always dangerous. So I had a bit of a search, and there doesn't seem to be anything which gives a plausible derivation for either phrase, still less specifies which one is correct. There's a fragment of an OED definition for "get shut of" and a couple of discussion forum threads, the second of which is from the excellent Eggcorns database; the main site doesn't have an entry for it, though. Many online dictionaries carry both definitions.

A highly unscientific Google test returns 108,000 citations for "get shut of" and 3,440,000 for "get shot of", which would tend to support my version of the phrase as the correct one. Hardly conclusive, though.