Three things control the tempo in Finale, and they work in a hierarchical fashion:

At the top of the “tempo hierarchy” is the recorded MIDI data Tempo Changes.

In the middle you have the expressions with playback effect Tempo.

At the bottom of the hierarchy is the Playback Controls.

Hence, to control the playback tempo via the Playback Controls,

1) Clear the MIDI data Tempo Changes (Edit menu > Clear Selected Items…)

2) Clear all expressions with playback effect Tempo.

I'm aware of much of that (and ended up just deleting the initial metronome mark). But previously, it was easy to just go into Playback Controls, override previous tempo markings by setting it to either "reset" or (use) "current settings." If that's no longer true, then what is the point of those options? 

There are no recorded MIDI tempo changes since I've been inputting notes directly. And regardless, I've unchecked all the Play Recorded options. I don't think I've been imagining this working as I described for many many years...

… MacOS 10.15.6
Finale 26.3.1.643 …

… previously, it was easy to just go into Playback Options, override previous tempo markings by setting it to either "reset" or (use) "current settings." If that's no longer true, then what is the point of those options? …

Unfortunately I have no experience with the Playback/Record Options.

Have you checked what the manual says about the Playback/record Options?

If the Finale Program does not work as described in the manual, then you should report it to the folks in Tech Support.

You may have found a bug in Finale v26.

Exactly. This is a bug.