The Cross-slide is likely to be a left-hand thread. Are they really 8tpi? surely both are more likely 10tpi (How are the dials scaled?).

If you have room, make two new lead screw nut for each slide thread them on the OD. drill the blocks and thread it to take the OD of two new bronze nuts. Use the OD thread to take up the backlash.

Alternatively, again if room allows, a new nut could be screwed on to the existing screw and fixed to the existing block.

Pictures would help :)