Solved! It turns out that I did need to increase the version number, even though it had never successfully signed. The Blackberry signing server decided that versions 1 and 2 had already been signed (though they hadn't), so I just had to keep going until it worked.
Error: Server response did not contain version.
This error made me think that that wasn't the problem, but apparently both errors mean that the version is already in use. Just keep incrementing the version number until it works.