Well, let me put my two cents worth in. I have limited knowledge on trannys, but I have a basic concept on how they work. What it sounds like is your clutch bands are beginning to slip real bad on your reverse gear. I have an 88 Chevy(duh) Blazer here, and it's begining to do the same thing in all gears, but it doesn't take no 15 seconds to engage. Now, the best way to fix it is to have it overhauled. I used to work in a shop that specialized in trannys, but it never rubbed off on me. Anyway, take to any shop, and they'll tell you that if one of the bands is wore out, it's best to go ahead and replace them all. I have a receipt from where my tranny was rebuild by the previous owner, and it was up around $300, but I would suspect this has gone up since '97. Hope this helps.
Robert