To close the loop on this thread:
I screwed up and bought both the wrong kind of Universal Joint and too few of them.
I bought two 1310 series u-joints at Advance, and I found out that I needed four 1300 series.
Charles saved the day by having two 1300 series u-joints on hand. Thanks again Charles
So I (well, more like Charles) replaced the u-joints in the rear. His vise was also destroyed in the process of trying to press out the caps. What worked out best in the end was the "pound out the caps with a hammer and a socket" method.
It also turned out that most of the play I was experiencing wasn't actually in the driveshaft but is somewhere in the axle. Oh well...in for a dime, in for a dollar-ish.
Thanks again to all for the advice.