II'll just share my ultimate solution. I too also noticed the little detent balls inside (1 on one side near the rim, and two in a row slightly deeper in on the other side of the jack interior. (A headlamp is very useful when inspecting the inside of this jack.) anyway, I tried exercising the spring-loaded detent balls but found it to have no effect. One ball did appear not to be protruding as much, but nothing I did to manipulate it with the paper clip had an effect. I figured there must be something in the recess with one of the detent balls, but was not coming out by simply pushing on them with the paper clip. So...
1) I turned off the phone to reduce the possibility of damaging it while doing the next step.
2) I used an air compressor (120 psi) with an air gun that had a needle inflator (the kind used to inflate basketballs and soccer balls) on it. these needle inflators always have the air outlet hole on the side of the needle, not the tip. So I simply shoved that into the headphone jack opening, all the way in, and moved it around a fair bit while activating the air gun to blow air all around inside the jack interior, focusing the air outlet on the needle to especially blow on each of the detent balls.
3) I turned the phone back on to test it and it once again worked properly, accurately registering that no headphones were attached, and properly playing my voicemails through the handset speaker. Success!
Hopefully this helps someone else.