She Moved!
After installing the transmission, deciding to take it back out to make it easier to fill with fluid, reinstalling it then deciding to remove it again to install the bits that make the clutch work, then installing it a third time, I was able to back her out of the garage!
So first and reverse definitely work. And I’m able to idle her in neutral without driving forward, so I think things are better. The seat and carpet are out of her so I can hose her out and put in some sound-deadening mats. Tomorrow night she should be dry enough to finish getting things together so I can go on a proper test drive. And so far, no leaks! Woo!