Nail in tire

[DrBacon]

So here's my predicament, one of my rear tires has a nail in the sidewall and cannot be repaired, however, all of my tires still have a pretty healthy amount of life in them (8/32"). Correct me if I'm wrong, but from what I understand having rear tires with different tread depths can cause some excess wear/heat on the differential. Normally I would just replace both my rear tires and call it a day, however I've been wanting to try a different tire as I'm not really happy with my current tires in the wet (Yokohama ADVAN Sport A/S). So the way I see it is I have a few options:

1) Replace both rear tires for ~$500 and prolong dealing with the tires being **** in the wet.

or

2) Replace all my tires for ~$1,000 (would be trying the Pilot Sport A/S 3+).