Here are the said updates. I added an additional fan to the base, as well as attaching a heatsink to the SSR. It used to get pretty warm.
I got it installed yesterday. The attic got up to the upper 70s, and the fans turned on once. Then, as the sun was going down, the fans turned off... once. That is exactly how I'd like it to function, so I'm thinking things are pretty much done with this project now.
Here is the unit with the additional fan.