So since I can specify with at maximum 15-decimal-place precision the course that the comets will take, I was forced to consider 2 different options to extend the orbital lifetime.
1. I could make course adjustments each time the interaction counter increments.
2. I could store the comet gravity variables at one interaction point, then restore them at a subsequent, very similar interaction point.
Both of these methods kind of feel like cheating, but after giving it some thought I have decided to try option 2 first, as it offers the quickest solution. Hopefully I can make it look good enough that nobody but the most anally anal will notice the tiny jump the comets make in order to have an endless orbit...
If I can't make it look awesome, I will try course adjustments...