I had similar issues with my basement RMH, which was explained to me as "Stack Effect."
To overcome this, I extended my exhaust up past the second floor, which is more of a neutral pressure zone. Further, I placed an "inlet" air vent pipe that comes from the basement exterior wall horizontally to my feed tube. Sometimes, to get the RMH primed, I need to open the basement door or a window, but once it's running, it goes quite nicely with no other opening, save for the air inlet and standard construction leaks.
Tightening the upper portion of the house reduces air escape, thus, reducing the displacement of the cold, high-pressure air from the basement. But I'm actually trying to use the dynamic to my advantage so that the radiant heat from my stove rises to the second floor, at least, if not the third, effectively.

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