Ah, I am so much more informed now that I dug into this topic!
I now know terminology: what the K-r has is a slotted lug. If it had lug rings I wouldn't be in this predicament, as the swivel snaps I had on the old strap would have worked. Jamming them through the slotted lugs put them off at a weird angle and the camera never hung properly, and that is what caused the strap to get in the way.
OK, anyway. If I get rid of the strap, I see two basic designs - a
strap that ONLY attaches at the (for me, anyway) right slotted lug and then loops around my right wrist, OR a two ended
hand grip that attaches at the right slotted lug and also at (or near) the tripod mount. If I upgrade the strap I can try the Peak Design Slide as mentioned above.
They all have pros and cons so maybe next step is to buy one of each that has been suggested here so far and mess with them.
Thanks all!