Try this for now, when coasting down a hill in “D” try putting the transmission into “2”, this should keep the tranny clutches engaged in the lower gear and should not cause the engine to stop turning whatever the problem may be…I have experimented with auto trannies without rear pumps. Tried this on a 74 and 76 Ford with the C-4 tranny and also worked on my 87 Mercury…Shut the key off during this when locked in 2nd gear and engine came back to life when key was turned back to run. I know this is not a fix for you problem but may eliminate the stalling going down hill and still maintain PB and PS…There is something wrong here with your situation, has to be spark or fuel or an air intake problem. …I know when these things happen on and off are hard to check if the engine starts right back up…What about the IAC, or MAF acting up can cause this…just a suggestion. if you had a fuel pressure problem it would appear when you are heavy on the throttle taking the motor to its max rpm. i wish i had more to suggest.
The only way you are going to find the problem is when the engine totally refuses to restart, then you can check it out. Good Luck.
EDIT: When I did this experiment If the the car was in “D” and was going between 35 and 40 mph, shutting the key off to on the engine it would not restart. Dangerous if going down a mountain pass. Locking it into a lower gear, engine always restarted ( or starting to turn again ) on its own. Now my 59 Thunderbird with the rear pump would always re-start even dropping down to 20 MPH in “D”. For those of you that want to know what a rear pump did was enable push starting an auto, which was driven by the output shaft of the tranny…Get it up to 20-25 mph, turn on ignition and drop it into gear. Most trannys past 1965 the rear pump was eliminated…Just a little education for you all…Take care guys and have a great day.