I've tried a couple of variations on what you suggest. Every one makes it harder to adjust.
but I gotta tell ya....the garda hitch looks cool, works OK, but I too am concerned about that tight pinch on the cord. Even on my 3.8mm Spyderline.... I'm pretty sure that the stress on the rope will be less if instead of doing the garda hitch you drop a ring, and tie a slipped buntline.
or a full turn with two half hitches, the last one slippery.
or take the extra ring and wrap it on the line as an anchor for a trucker's hitch, then back and forth and a couple of half hitches...
all of these are a lot faster and more flexible than the HH wrap. Just use the ring(s) as a tie-off assist.