Is this amount of record/tonearm bobbing "normal"

Your platter looked out of round or out of balance to me as well.

Agree - platter looks out of true - not seated properly on the spindle/subplatter

Thanks for the feedback. In this case there is a lower platter, an upper platter, a mat, and the record. The lower platter is about 48 hundredths "tall" and you can see it in this video:

https://youtu.be/0Tq1hydi-DI

The runout (probably the wrong word) seems like it's about ~three hundredths. 

I can hear it on some records. I guess my choices are a new platter or a better turntable.

Yes, millercarbon, it is a graham tonearm. I love it. 

+4 for MC, slaw, and Dover.  Watching the bottom edge of the platter as it rotates through the window for the speed sensor, it looks to be moving up and down, as MC notes.  The top edge of the platter proper (not the mat or the LP) appears to be unevenly machined.  The champhered edge changes shape a bit as it rotates if you concentrate on one point.  I'd worry about the platter first; no big deal if an LP is warped or off-center; they are nearly all imperfect.  Could be the platter is askew with respect to how it should sit on the spindle; that would be the easiest thing to fix.

Wobbling up and down like that is bad, but ultimately not that bad in perspective, considering a lot of LPs are like that anyway. Would be worse if off center as that would generate speed variation or wow. When you say "with extended chords sound bad, uneven" that's probably the reason why.