Is this amount of record/tonearm bobbing "normal"

+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.

It’s actually tough to tell if the entire platter is actually fluctuating or if it’s just the machining is off giving the illusion it’s the entire platter. I would pull your mat, it looks to be a big contributor in this. Otherwise, what everyone else said is correct. Records are rarely dead flat. 

platter cover is definitely rising/lowering

could be it, or primary platter below.

remove it, check primary platter, warped, misaligned?

make a vertical grid to view thru

or, buy one of these

https://www.ebay.com/itm/174856306267?_trkparms=ispr%3D1&hash=item28b63f7e5b:g:QkQAAOSwbdNhAAR2&amdata=enc%3AAQAGAAACoPYe5NmHp%252B2JMhMi7yxGiTJkPrKr5t53CooMSQt2orsSDAeS9EQtjPGVfKXTxF0%252Bjrdzwkj9GJsoGQFbDHXg2HjJbbo4koBqVZV3aUKhII9o9NpHms2YGhQzTNWQjKZkfkT46oS0M6F6gjTDHGIU9T%252BNd0uakf2G1tT%252By%252FHRxgzYDNlkM1lWIh3N0CRi%252Bz%252FTfjw8YGzCIglr8AZTQ7KpCoAXIFlmrzvI7TSNXNqsilUNmZytu4ICXPcXEcmIvqWbEdwIs3hpgqsJpcplc56PfJfA60KXwt49igcg31UOhJQe5ZO4u%252FS93%252BP00G1Zuk6DhfBI%252Bgjk8fj7A3F%252Fw%252BbL59KOXvyU4kge69KDASEChNoXJtKVqvMnmGDrpcs93QWsIzeFvJ6LC5hbopuo2SX%252F87TQdOG%252FRYyxaRZex%252Fp4cpOzekGdV4ppdLQGK6LUfshBlXZFM8a%252FQEXSpNqLDbjNSUIhX8yzlj5fn2nfNRqp9fgLF3ElXx4MrgnJG6SvKEUrqZfzv2gNDOCMv8hhkFquhrKCxBRbuD0dykHDRfuMB8rNf91i8Wr37C5H7MZsdm3Nlx%252BeokX6iSSMST9TWBiprOUSX9w5ebrKc0JcSE3w%252F1NJ2fRdLeMvxhbsXGCtuBrk6T7twGKDjXcwBqDz5F%252Bf3ckWqe31US%252Fiv4iaWMV1kyR2iWiPNxraLe3n3zlvCAIT4eWu0N7%252B8j57WpmC92jPOqVwvBnuxutYoGd3vHS0mIuJvtSyRR0sOAaSvMX2xHUDtWGY2n2wgfnwlwLY05nk8QNdHo8f2Tfy8gOtHq35pPAR97dJ%252BdoWSk8E7U934JAiFO%252FMBm9XdQ8okAYtuhMsLJvqCqjOLFxUcCzfI2lpBGTmcexNccFJ80FfHhjg5qJvuA%253D%253D%7Cclp%3A2334524%7Ctkp%3ABFBMupj1-MVf

Try doing the video with a tripod supporting the phone. Your handheld video even braced to the table is too unstable to accurately judge the platter wobbling or not. To me this looks pretty normal but you’ve got some pretty great items there and I can understand you wanting it right.