I did briefly look at ERVs, but for a single room in an apartment building with central heating, that level of energy recovery is probably overkill. I'd be simulating the result of keeping the window slightly open, I don't mind the cold it's even better for sleep (and the heat is not a problem here).
But your core points about the system's location are a real lightbulb moment for me. Having the fan up by the window instead of as a trip-hazard on the floor would be a huge improvement.
I can remove the housing for the trickle vent. It's screwed on, so I can put it back later without violating my rental agreement. Then, I could 3D print a custom adapter to fit that opening perfectly, designed to hold one of the Noctua fans and a small HEPA filter like you suggest.
That feels like a much more elegant solution. Thanks for the inspiration! You've got the gears turning again.