I have done it many, many years ago shrinking liners into cylinders heads for valve stems. As I recall my interference was something like 0.0005 on 0.5000" diameter.
Your 0.004 interference on 3.500 diameter may not be possible because liquid nitrogen is only about -196 degrees. Have you done a calculation for the shrinkage you will get with a 200 degree temperature change.
Anyway, whatever interference you use will be very close to the reduction in your ID if the end block is signficantly thicker than your sleeve.
An open mind is a virtue...so long as all the common sense has not leaked out.