Should an Officer who was non-selected for promotion, and discharged at 16 years of service, reenlist to finish their 20?

Yes Sir, you should Skipper.

Yes, another 4 years and at retirement they would still retire at the Highest rank held. I've seen Officers who were passed over a third time and then held enlisted rank until they actually retired and did so in the highest officer rank they had served in. One Major I knew entered the enlisted rank as a Tech. Sergeant, (Five stripes) but once He retired it was a a Major. It was interesting also seeing Him wear pilot wings on and enlisted uniform but as an Officer He had actually been a pilot and earned those wings. He did end up being a pretty good NCO after His service as an officer and in the enlisted field did get promoted to MSgt.

Yes. Other alternatives include a government civilian job that will let you count military time served toward the civilian pension. I RIFed and enlisted back into the USMC as a warrant officer to finish out 20 for his pension. I also had an NCO who told us repeatedly, "anyone who gets out under 30 is a quitter."

Absolutely. I would not hesitate a moment to be, or advise another to be, a "gentleman ranker" as they were referred to in the British army.
I worked with a WO who quit the Army with just a few years to go, in hopes of saving his marriage. It did not work, so both marriage and career were a "blivot". He was too old to enlist in the Reserves when I met him, so even that was out.

one of the less cerebral choices i made was not staying in the reserves; wouldn't be big, but that small check would help make things easier now

No! Take all the benefits you may or may not have accumulated. Be sure to document any and all past and current medical issues, Awards, Time in Service, Time in Grade, Overseas and Foreign service, and Officer Performance Reports on your DD Form 214, Discharge Document. Then accept the discharge, get out and then run for the highest political office you feel comfortable with. As you rise in the political hierarchy, use your status to challenge those higher grade "know it all's" who by the luck of the draw in many cases were rewarded for their "Me Tooism's" careers. Learn how to operate with a "get even with" attitude, because it may be how you got non-selected for promotion. Be sure to start a Veterans' Administration (VA) claim for any and all medical issues. If the claim is denied, keep the documentation, because believe me, as you age many of the denied claims will become very real and easily verified (if you live through the emergency hospitalizations).

There are far to may factors in this equation for simplistic answers provided by a panel of Rally Point "Experts". Do your research and find out what is best for your specific situation. First step would be to seek the advise and expertise from a Recruiter. He or she can sift through all the piles of what-ifs and give you some valid guidance.

Absolutely. As an Enlisted Officer (Sergeant First Class) I served with several other Enlisted Officers that had been Commissioned Officers that had gone through a reduction in force. Finish out the 20 and retire.

Yes.

I went back in.