I'm not sure you'll find a through-the-window HEPA filter, but I think
you could jerry-rig one easy enough. Building a small, light frame
that is the same size as a filter and put it in your window and seal
it up. Then put a fan on the inside to suck the air in through the
filter. Then run the inside the room filter, too. Run the window
filter 24/7.

This is what I was thinking, but I was not sure how strong of a fan I
need to suck through a HEPA. After all, a HEPA may be an overkill.
Also, since complete filters are so expensive I was thinking may be
there is more to them than just a fan and a filter.