I discovered some things through experimentation today, and if anyone is interested in doing this in the future, here are some tips. Some of the online tutorials are OK, but there are things about it that you need to know to get it right.
1. If moving beat markers in the clip's timeline to the right, make sure to clear space for them by moving other markers to the right to make room. This is what caused some of mine to lose their numerical value.
2. Disable any markers that are not on the transients that you want to derive your tempo from. Make sure if you going after a quarter-note based time signature, that only quarter-note markers appear and are then aligned.
3. Listen and watch over and over to ensure that your remaining markers are where you want them and that the clip's beat markers are aligned and locked with them. They turn yellow when properly aligned.
4. Click on the Set Tempo from Clip button. In my example, I had it set to Beat not Measure or Clip. It aligned that project time line with these markers perfectly! (I surmise that had I placed and aligned markers on the first beat of every measure that I would use the Measure setting.)
Hope someone finds this useful at some point.