After a lot more testing of the shielded loop and Mobius loop designs it became clear that they gave no improvement in noise rejection over an unshielded loop.
The design of the Loop Antenna Amplifier in the later "+" and "++" versions gives a tightly balanced loop input that helps reject common mode reception from the loop element. The early HF/VHF version also had a similar input design.
In all versions of the Loop Antenna Amplifier there is a common mode filter on the coax output to reject common mode noise coming up the feeder to the loop element.
I suspect that it was the common mode noise coming up the feeder that made the shielded and Mobius designs appear to have lower noise in amplifiers that didn't have good common mode rejection.
It's far better to stop the noise before it can reach the loop antenna element.