Ignition or Temperature for stall and hesitation?

1986 Lincoln Continental 5L 93800.

Recently I posted the initial issue with my car; Jittering engine when it’s warm.
If you wish you can check it out before addressing this one.
However now the car is at the shop.

In the discussion I shared that it seem to hesitate/jitter when it ‘s warm after 20 miles or so, then it began sooner, then it began stalling at idle. The story is on my first post.

The car’s was towed to the shop Monday.
The car stalled for them like it did for me.
One thing they noticed is that after it stalls and you try to restart the car without bringing the key back to it’s off position it won’t start the engine.
It tries to start just but won’t actually start the engine. It sounds like you have a bad starter or may have flooded the carburator which this car does not have.
Bring the key back to total off position and start, the engine starts no problem, then it stalls within 2 to 3mns.
They suspect an ignition issue.

Before they began any testing I requested they change the fuel filter which was way overdue.
The old one was not clogged.
Hesitation is not due to a clogged filter.

Service and Parts done and changed in Oct 2015 before towing and problem occurrences are listed in the order they were done / happened:
10/6 - Tire pressure, balancing and rotation
10/7 - Motor Oil and filter
10/8 - 1st Smog Check failed – Needs timing adjustment
10/10 - Motor on 2 doors fixed – killed battery – recharged – cranked
10/12 - Drove car about 40 miles before appointment to adjust timing and 2nd Smog Test – Car
Hesitates strongly at off Ramp. Must fix problem before re-smog
10/17 -Tune Up done – New plugs, wires, distributor cap, rotor – tested 5 miles only – no hesitation
10/19 – Drove car about 15 miles before appointment at Smog Shop – New Control Module (cracked
fell apart), 1 new vacuum hose, timing adjusted.
Passed the Smog Test
Subtle hesitation resumes when leaving Smog Shop. Mechanic doesn’t know why.
10/21 - Subtle hesitation within 6 miles (sooner then before).
Added 15oz can of Total Berryman + fueled up.
Hesitation significant especially on slight upward grade (am in hilly area)
1st stall at low idle when pulling out of store parking lot. Cranks back up
Once home, left idling, stalled within 2 to 3mns. Stopped trying after 3 times
10/22 - Car stalled at beginning of drive up of driveway with a 40% grade.
Back in car port, idle, stall. Stopped trying after 3 times.
10/24 – Cranked car, slight hesitation noted, revved up slightly for a few minutes. Decelerated slowly,
car began hesitating, foot off gas paddle, stall.
10/26 – Towed to shop.
Car stalls for them and they notice is that after it stalls and you try to restart the car without
bringing the key back to it’s off position, the engine won’t start.

Since at the shop using up to date testing equipment, own visual observation and listening, diagnostic diagrams, these following tests have come back negative:
Fuel pressure shows normal
Electrical wiring in engine test good for being grounded and performing
Hall effect sensor
Temperature sensors
Vacuum hoses
Main computer in dash board
Even ignition
These are the tests I’ve retained they conducted. They’ve looked at more than that.

At one point at testing, the car stayed cranked and ran for more than 5mns before stalling.
They then focused on temperature issue.
But the key position issue described early is still present.

So Temperature issue or Ignition or something else that has an effect on both?

In order to save me any more expenses which have added up, they’d really like to find the problem through testing before taking apart anything, however they might throw the towel in sooner than I’d like. My problem cannot take precedent over other newer cars with issues easier to detect with their equipment.
It’s an old car that’s otherwise in good general shape.