Weird noise after 4 speed install

It wouldn't (shouldn't) cause the noise you have, but from the video, it appears your pinion angle might be slightly off. Going with the longer driveshaft needed with the manual, did you measure the pinion angle and compare to what you had before? Might need some shims on the rear axle. It almost looks like there is a bad pinion bearing letting that yoke move a little, is there any side to side or in and out play on the yoke if you try to move it around?