Two points I didn't notice here (though I may have missed them).

I try to say "Passing on your left please." The leading word "passing" announces the upcoming event and serves as an attention getter before the crucial word "left". The word "please" announces it as a request rather than a demand, and anyway, people usually respond better to courtesy.

The time element is important. What bothers me as the recipient of an "on your left" warning is when it startles me by being unexpectedly loud from someone unexpectedly close. Such warnings come so close to the time of the actual pass that I wouldn't have time to react anyway. If I'd known that rider was there (which is usually the case but not always) he/she wouldn't have needed the warning anyway, but if I didn't I'll need more lead time than that.

+1 on MUPS. Yesterday along the Charles River I had to pull off the path completely and stop and wait because some 30-something guy was walking towards me backwards 30 yards in front of me. His wife (or SO or whatever) eventually got his attention so he turned around. I smiled at them because I thought it was amusing, but he gave me a sour look like I'd done something wrong. You wanna' walk backwards along a dedicated bike path, it's your own mistake, buddy.