OK, so I've figured out another piece of the puzzle. Well, at least I think I did!
It appears that some aquastat controls BREAK on temp rise and some BREAK on temp fall, and some do both. I noticed a lot of Aquastat specs talk about SPST and SPDT switching.
The link you sent me was an SPST which breaks on Temp rise.
I nead either an SPST which makes on temp rise or an SPDT switch. An SPDT switch is basically a toggle switch. On temp rise, one side makes and one side breaks. I would just use the side that makes on temp rise.
This was a good link on switch definitions.