Bits and bobs :
1) heat from the cooker :
Have you tried using stack effect to draw more air across the surface?
e.g. Grab a 4-8 ft piece of ducting from the bone pile or wherever and hold it a few inches above the hot burner area ( maybe with a stand or hanging from the ceiling ) . It
should help get the heat away from that area. If that works more would work better.
A solid maybe.
2)
De humidification :
Intentionally leave one of the windows without a cover to get the
water condensing their first, then figure out how to deal with _that_ window condensing. Possibly a metal plate rather than a window. Possibly placed in a cold sump / the lowest spot in the area so that the cold doesn't drain the rest of the structure of heat, but can be allowed to get cold
enough to dehumidify then let the water flow down ( and out? ).
Good luck!