How can one fly a stabilized approach when the final approach path is curved?
Perhaps my thinking is now considered outmoded (retired in 1999), but for me the definition of a stabilized approach doesn't preclude turning, but only that the turning (when necessary) is accomplished at a stabilized rate. The idea was to be setup in landing configuration, at your stabilized final approach speed, sink rate, and power and tracking whatever the approach path is from the FAF down to the landing flare.

For tracking DME arcs, we were taught to find that angle of bank that (given our final approach speed) produced the desired turn rate. We would hold that bank, just as we would hold wings level for a straight final approach path.

If the DME started in increase, steepen the bank a little. If it started to decrease, lessen the bank a little.