This thread explains the terminology in a bit more depth, but essentially poles are independent circuits contained in a switch, and throws are the number of electrical positions in each one.
…push-button normally-off momentary switches that can turn on both circuits at once.
Then you’d be looking for something that includes an “Off-Mom” switch function, with two poles. You said you wanted pushbuttons as opposed to rockers, toggles, etc. and I’m assuming that something with a bit of environmental resistance would be a positive as well. Accordingly, I’d suggest that these would be among your better choices.
The toggles you ask for would indeed be DPDT as you guessed, with a “Mom.-Off-Mom.” switch function. These would probably be good candidates. Toggle switch boots are here if yo’re interested–make sure to select something with threads that match the bushing on whatever switch you choose.
Regarding heatsinks, it’s a question of what A) gets the job done and B) is convenient mechanically. I can only guess at electrical loads and have no clue what your mechanicals look like, so you’re sort of on your own here. That said, an electrically insulating thermal pad such as BER204-ND might let you get by with whatever frame-mount arrangement you had before, provided your mounting hardware doesn’t short things out. Best bet is to clamp the transistor body directly, and forget about the hole. While perhaps a bit sketchy due to risk of cut-through either during installation or by vibration over time, it’s a definite step up from paint and thermal grease… Other option is to find yourself a standalone heatsink of convenient form factor that you mount in electrically isolated fashion somehow. Assuming you need to get rid of 10W without any forced air, I’d guesstimate you’d be after something roughly fist-sized. We have heatsinks listed here and here. Worst-case operating conditions will probably be with output equal to half-input, so if you can still hold a finger against the transistor tab after a period of operation at that point with load connected, you should be in decent shape.