I use 1/4" copper water line and 1/4" brass compression fittings.
Not sure what you got going on there with the 3/4" plug, but could you adapt a "T" fitting to it so you could put a plug back in one end of the "T" so the cap could still be removed to drain the water line?
Unscrew the plug and screw in a 3/4" 'T' fitting, just a thought...
I'm not much of a plumber.
In any case I would adapt the 3/4" MIP to 1/4" compression and from there run 1/4" copper line to the refrigerator.