Just a quick update to say that I heard from the mechanic at Ted Porter's Beemer Shop. The water pump is A-OK, so the next thing to check is the head gasket.
They went ahead and ordered a new one, which should be at the shop by this coming Wednesday.
In the meantime, they're stripping the bike down to the engine head and said they'd give me a call when they can tell for sure whether it's the head gasket.
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