Automatic not rolling in reverse (search engines no help) any DIY suggestions?
 

Hi, I was leaving work, and was trying reverse out in my 99 SC300 automatic. Although it's clearly telling me the car is set to reverse on the dash; when I rev the car, it doesn't move. It rolls forward in drive & neutral. My check engine light has yet to switch on. I have noticed hints at a trans problem:

- hesitating and jerking to move in drive at a full stop when on the throttle
- car barely rolling forward at a cold start
- gradually longer hesitation (still under a second though) in gear shifting, but no shifting in to the wrong gear
This only started after I hit 147k miles, but have had no problems, transmissions-wise, before. Checked my transmission fluid; it's still half full and cherry red. I've tried looking it up, but most results are either assuming the opposite of my problem (car moving in reverse and not in drive) or that the dash doesn't tell me I'm shifting in reverse, which still does.

I know many are gonna tell me the trans is dying and needs a rebuild, but I just need to keep the car functioning until I leave for the Navy in February. Two parts I've been told could be the problem are automatic transmission solenoids and the neutral safety switch. I'm doubtful of the latter since the car cranks in park and neutral no problem.

Any suggestions are appreciated, thank you.