Just looked back over our conversation. Have you ever had the tranny serviced?
Not tough, just drain the fluid and change the filter, then fill it back up.
Could be low on fluid or old ("watery") fluid....of course, if that were the case, you'd think you'd have other problems on top of just coasting too fast down a hill.
odd that you have to push on the gas to get it to grab and start braking, too.