I think I understand your setup. so, let me suggest what I think I would do.
first, make sure you have a GOOD face mask/respirator with charcoal canisters, not dust filters. I bought a mid-priced 3M model that has interchangeable dust filters and carbon canisters.
could you leave the door open from your garage to your house overnight, to get the temp in the garage as low as possible? IIRC, it took me about an hour to varnish (roll and tip) the entire outside of the cabin. so, if you could start first thing in the morning, you would close the door to your house, keep the garage door closed, and hope the temp doesn’t get above 80 in an hour. you’ll be wearing your vapor mask, so working in a closed garage for an hour is no health hazard for you (assuming your mask is intact, and you can’t smell the varnish when you’re wearing it). I happen to have a small window AC in my workshop, and I didn’t open the garage door until I was done varnishing. then it airs out pretty quickly.
to be doubly safe, although I doubt there is enough vapor in the amount of varnish you’ll use for each coat, I would make sure there are no sources of ignition in your garage during the hour you’re varnishing.
you didn’t ask for varnish technique advice, but I’ll offer what I learned.
I wasn’t happy with the results from using a foam brush for tipping as suggested in the hymnal. I did some reading and learned that I should use a badger-hair brush for tipping. turns out these are as rare in retail stores as are badgers themselves. supposedly an alternate is a “china bristle” brush, which is boar hair that is specially trimmed to simulate the softness of a badger brush. first try with a Wooster brand china bristle from HD was unsucessful. the bristles were too firm and left brush marks. second try was to go to a sherwin Williams store where I found a “badger” brush, Red Tree brand, that was not really badger hair, but was china bristle that was supposedly as soft as a badger brush, and the tip was properly trimmed/beveled to use for tipping. I was very happy with the result. if you have enough lead time, you might find a genuine badger brush online. finally, I discovered that Home Depot has Wooster 1/8″nap 7″ roller covers via ship to store.
they are in pkg of 2, for $2.34 per package. my local woodcrafters charges 11.99 for a package of 3!
ken