I'd hold off until you have a new transformer. I've seen a few other threads here where people had no vertical, and the line often looked a bit skewed.
Once you have an actual picture, you can then display a test pattern/grid to aid in adjustments, and do all of the convergence/purity stuff in one swoop.
If memory serves, you can "rotate" the picture by rotating the entire convergence assembly , as that will adjust the directions that the magnetic field deflects the beams.
There are usually a set of rubber wedges under the yoke to keep it from moving. You should mark their positions before you remove them, otherwise your centering will be off when you reassemble.
Here's an interesting read while you wait. This discusses purity adjustments on newer colour CRTs, but the principles behind it still hold.
http://personalpages.tds.net/~rcarlsen/cbm/converge.txt