I learned to rebuild NP833 from a factory service manuals years ago when I drag raced a 1970 Baracuda with a Hemi and 4 speed in NHRA stock, you can to The hardest part is changing the 4 sets of needle bearings in the cluster gear, all the other regular bearings, both of them, are pressed on and off I use to remove the rear bearing snap ring and then use the 1st and 2nd gear weight to push that bearing off by dropping the rear of the output shaft onto a 4x4 block of wood, worked good, never hurt a part I would drive it back on with a steel sleeve or another used inner race and a brass drift and hammer I ended up buying a Snap On bearing remover collar to remove the front bearings off of the input shaft with a home made press, it works good on the rear axle bearings also BTW, I'm not sure that noise is a bearing noise, truthfully
I'm typically the same way, but not with transmissions. I've had them apart just to see how, but the interest ended right there. :-) I don't have the patience (or the luxury of time) to rebuild this one, especially since it was a freebie to begin with and nothing special.
I'm not sure the noise is, well, anything specifically - I've just arrived at that conclusion by eliminating what it couldn't be - and since nobody has come up with anything else better, it'll get yanked and replaced, to be sorted out by someone else later maybe.
Question stands - who does the better rebuild, Brewer's or Passon?
