x2 on what Wren'* saying. Your problems do sound like the wrong tranny for your PCM. I think we should make absolute certain of this.
Find the RPO code sticker on the spare tire cover in your trunk, and ideally post us a pic of it, or at least find the gearing code for us. It should be one of these on a '99 SLE n/a:
FQ3 - ratio, transaxle, final drive 2.86 (w/hi stall)
F83 - ratio, transaxle, final drive 3.05 (w/hi stall)
Then go up under your new tranny and ideally post us a photo of the tag or at least write down the first 6 numbers (going down, next to the barcode).
Pattern should be: "61yxxx"
y=year, xxx=3-digit gear/stall code
After the 61, it should be one of these:
8YFB (2.86 / lo stall)
8TPB (3.05 / hi stall)
9YFB (2.86 / hi stall)
9TNB (3.05 / hi stall)
2004 Buick Lesabre Limited, Gran Touring; Bone Stock
1998 Buick Lesabre Limited, Gran Touring; Mods: Poly sway bushings/endlinks, Tru-Cool trans cooler, Thrasher shift kit (med), PLIM, front PEM; Mods in progress: Alot of stuff, but slowly...