...I suspect a lower impedance line eases the pressure on the tuner in this case...
Common T-network tuners tend to be more lossy at low impedances (below 10
ohms or so) and more efficient at higher ones, especially on the lower bands.
The 10m loop used on 20m will have a very high feedpoint impedance - if you
connect a feedline at that point it should be a high impedance type (twinlead,
etc.) rather than coax. You might have to shift the wire lengths a bit if your
tuner has trouble matching it.
If you connect 50 ohm coax to a 1000 impedance load, a quarter wave later
it gets transformed down to 2.5 ohms. The same length of 300 ohm line gives
you about 100 ohms instead, and is much easier for the tuner to match.