I feel your belt tensioner isnt tightening it enough. The reason why i say that is because belts stretch after a little use, since you cant manually adjust the belt tension on a 2JZ. You might want to warranty your current belt and go again with a new belt. If it does the same i would go for a new tensioner and call it good. On cars with manual adjustment of belt tension i over tighten a new belt so once it is stretched it gives it just the right tension for it to not squeal. What brand are you using? just curious
GL

 

take the belt off and clean the pulleys/surfaces.
It's squealing becasue its slipping, it's slipping becasue there's somthing inbetween the belt and the pulleys.
Get some brake clean and go to town.

 

So looking at my pulleys, they need a cleaning...still don't understand why this would just pop up after an alternator swap could the mix of dirty pulleys and shiny new ones be the reason?. Also I'm assuming the belt gets warm and sticky which stops the slipping?

 

yes, the belt will transfer oil/dirt/ or whatever is on there to the new pulleys.

like i said, just pull the belt off and clean everything throughly. should only take 30mins max.

 

I've got a similar issue. Accept mine gets a really loud screeching noise when I turn on the AC. Doesn't happen all the time when i turn on the AC but it does happen. I am also starting to notice on a cold start right when i start it, it does have a small high pitched screech right at the beginning. Could this be the same issue?