Why do these tail-sitters not have bigger propellers in their main engine?
You're correct that it is more efficient to accelerate a large mass of air to a slower velocity. But then there are other things to consider here:


The attitude control i.e. transition is based on the downwash generated by the propellers (unlike helicopters). Either you should have high speed downwash or reach higher speeds for the flight controls to become operative. Reaching higher speeds in vertical flight would tax the engines further and the higher speed propellers, however less efficient would have been the better choice.
Huge rotors, like in helicopters would've been efficient, but also bring the related problems of blade flapping, lead and lag and droop, especially leading to problems during transition. There are also issues with tip speed, especially for the high speed interceptor role these aircraft were intended for.
One of the design considerations was shipboard (even submarines were talked about) use, conditions in which higher diameter rotors would've been a headache- you have to find ways to fold them, for one.


In the end, use of smaller rotors would've been influenced by a much more mundane reason- availability of powerful engine. Note that both of these aircraft were powered by variants of the same engine- modified Allison T40 turboprops, the only engine rated for vertical takeoffs and landings available- which consisted of two Allison T38s lashed together to run the same gearbox with contra-rotating propellers.

In fact, the heavier Lockheed XFV never made the transition flight, waiting for a higher powered T-40 and did only horizontal flights with long landing gears (which would've precluded using higher diameter rotors- though I'm not sure if that was a consideration).