I have some problems with my '93 previa transmission. Can't get on reverse quick, it's sleeping when cold.

Mine is kinda of sluggish until it warms up. Than it runs fine.

When was the last time you had the fluid changed?? Does wonders

I agree. Change the fluid. Even if you just take the drain plug out, you will get 2.5 quarts out, or so, which totals to about half of what is really in there. I do mine every 15k, for the few dollars it costs. Make sure you have no leaks around the tranny pan. Even if you take a 10mm wrench and tighten up the bolts, that may help. If they suck air around the seal, that could cause slow shifting. I would not bother changing the screen, mine looked so much like new after 300k, that I would consider it a waste of money. I had a dealer tell they do not go bad, ever. I did not believe them, but after 500k, I now conclude that they are right. Make sure to grease that little grease fitting on the far back of the rear driveshaft. That could be your reverse trouble. And, I would check the 2 small hoses on left and right bottom of the radiator. That is the tranny cooler unit, which I think all Previas have, and probably the reason the trannies last so long. You can use 5/16 tranny or radiator hose there. That is another place that they leak, and suck air, depending on your mileage. These are inexpensive fixes, and will probably help.