I use an original Nokia headset (the old ones from before the crash-and-burn), it works very well. Finding them could be an issue though, I got mine from the junk bin at one of those phone repair places, it was brand new and still bagged.

I'll keep an eye out for more if you want.

Thanks for the offer, but I think I'm on a different continent from you (I'm in California).

Ah yes, you are, I'm in Europe. The one I have is called the HS-45, the multimedia controls don't work with my current phone but the basics (mic, headphones, break connection and volume) do.

You might get better luck with mic-in-cable jacks, my headphones came with one (TRS plug on headphone side, TRRS on other) but they can be bough as separate items.

Microphone/headphone combos with a single TRRS jack are fundamentally going to be poor, because the microphone line isn’t balanced. Microphone signals are very low level and pickup noise easily.