Welcome to AF.
If the valves are sticking I would suspect you have a hard part grinding up or worn out and throwing grittie metal in the valve body.
Was there metal shaving and ground up metal in the pan and filter?
Valve bodies can be cleaned and valves polished up.
Along the years they have a TCC clutch apply valve kit to take care of the 1870 code. and slip problem.
Sonax web site has the repair kit for the valve body.
If you are going to rebuild it take it down to bare metal and clean up everything good enough to eat off of.
Then inspect every thing for wear.
Replace all worn hard parts and bushings and planetary gears and thrust washers.
Update the sun shell.
Get the acc kit for valve body.
Replace the converter with a good quality one.
And be sure to flush the rad transmission cooler.
Get a transmission hand book and go threw the repair procedures and updates.
Go threw the front pump real good.
Use good quality clutches and seals.
Replace all sealing rings and a special seal installing tool is required to do that job.
The old days of throwing a 40 dollar kit is over.
Your cost may run 750-1000 dollars for a good quality rebuild if done right.
if the transmission is high mileage and worn bad.
http://72.19.213.157/files/4L60ERepairs.html
http://72.19.213.157/files/4L60ERemoval.html
