1997 Cadillac Deville

My 1997 Deville has 96,000 miles. Automatic transmission and the Northstar engine. I have a problem that has stumped the best Cadillac mechanic in Atlanta. This started about a year ago. It is intermittent, once a month, once a week, twice a week or twice a day as last Saturday.
It always happens while coasting to a stop, foot off the gas pedal, applying brake. The engine dies as though I cut off the switch. No missing, backfiring etc, it just quits. I shift into neutral and start it most of the time while still coasting, it cranks and I continue driving. Yesterday I had to pull to the shoulder and it took three attempts before it started. It has run fine since.
Answer this question and I promise a generous donation. I am to the point of trading cars.
One other thing, my fuel gauge will get down to 4 gallons on the digital read out and then start going up until it shows a full tank, when in fact it is empty. The only major problem I've ever had was just over a year ago the whole digital dashboard information center (miles per hour, fuel, dic, etc, fried. It was removed repaired, recalabrated and reinstalled. Thanks! Dan