For the moment, I would suggest not to worry about DWPS/UWPS, but just try to use the motion you showed at the start of the video and see if you can use it to play some simple (but fast ) musical phrases. Just to keep things simple and get your foot in the door of speedy playing!
As far as I can tell your tremolo picking is a downstroke escape motion, so it should work well across different strings when the last note on each string is a downstroke. We can test this straight away: instead of the PG lick, which has the “lone note” complication, why not try this sequence (or anything you like that only changes strings after downstrokes)
B-5-6-8-------------5-6-8- then repeat: 5-6-8-etc.
D U D U etc.
Indeed the hand sync is a separate challenge from the problem of changing strings. One thing that seemed to help people around here is to do some artificially strong accents on the first note (or each note that lands on the beat). For example, in the exercise above you could accent the first note in each group of 6.
For starters, it may be useful to focus on syncing only that note, allowing the ones in between to be a bit sloppy.
Again let us know how these things feel when you had a chance to try