I have to thank @ProfessorSparkles for getting me to this solution, which doesn't require saving and reimporting, or making a duplicate of the source footage. Here are the steps:
1) I started with the 2 clips I'm using in the same bin.
2) Drag the landscape-oriented clip to the timeline. That creates a sequence with landscape orientation in the bin.
3) Select the clip in the timeline and delete it. (The sequence is still in the bin.)
4) Select both of the clips within the bin.
5) Right-click and select "Create multi-camera source sequence...."
6) In that dialog box, click "OK". Premiere will synch up the 2 clips.
7) When I first did this, it asked me a question before creating the sequence. It was something like, "The settings on this sequence don't match the existing sequence. Do you want to keep the source sequence settings?" CLICK NO. That will make your new sequence match the settings (landscape orientation) of the existing sequence!
8) You can then select the blank sequence you created a minute ago and "Clear" (delete) it.
9) Drag the new sequence to the timeline.
10) Hold down Ctrl or Cmd and double-click on the new sequence in the timeline. A new sequence will be created that shows each clip separately.
11) In that new sequence, select the clip with portrait orientation.
12) Go over to "Effects Controls". In "Motion", rotate the clip either 90 degrees or 270 degrees.
What a relief it was to figure that out!!!