Sounds like the linkage is set in the neutral position on the tranny when in "P" and your motor mounts could possibly be failing allowing the tranny to shift into "D". I've heard of ghostly shifting because of worn motor mounts.

Your tranny is robust. I would flush and refill the tranny with new fluid and monitor it over a few hundred/thousand miles. Check the level and color. If the color starts to get dark then your clutch packs are burnt from running on low fluid levels. Worst case if you're handy is to get a good donor and install it.