Build a squarish CoreXY gantry with spectra line or steel wire rope.
Take a pair of screws each with travel = about 75% of the X or Y axis length.
Attach a pulley to the screw nut to make a 2:1 compound pulley / block and tackle.
Screw travel produces 2x line travel.
CoreXY gantry requires sqrt(2) = 1.41x line travel per nozzle travel.
Thus, a screw that fits within the frame can produce full CoreXY gantry travel.
I suspect you could jury-rig a way to use the Y axis (stationary) CoreXY rails for the screw nut carriages by adding some rail length. Which would look rather interesting. But hiding them in the bottom of the frame is probably more reasonable.