I recorded a measure of MIDI notes to be used as a basic drum track. I then selected those notes and used the repeat function to make an additional 79 copies of that measure. The notes were successfully repeated, but they did not align correctly with the the following measures. How do I make copies of a measure of MIDI data then get them to align properly when I use the repeat or paste function? 
Did you do this inside the drum/key editor window? Because if you just select the EVENT(blue/yellow/green/whatever color) in the project window (the one that shows all your tracks in the project) and then use the repeat function, it should work. I do this all the time.
In order for this to work, you’ll have to be sure the EVENT is trimmed to the one measure you want. You may need to trim it (with the scissors tool) to get it like that.
I think you mean a part, not an event…?
You are correct. My bad.
And the project contains varying tempi…?