Its not obvously the pressure reg, but its the only thing I could think
of that might 'run out' a bit like a carb car running until the fuel in
the carb ran out if there was no fuel supply.  Possibly its suddenly
releasing pressure.

You have already eliminated fuel system blockages in the main areas,
could there be something in a pipe?

It must be something faily blatant that is causing total shut down, I
guess the questions are:

Is the Engine Mgt shutting it down due to an out of spec sensor (eg
crank sensor)?

Is a key running system diing, ie fuel or spark due to.. eg an
electrical fault heating up for some reason?

Restarting straight away would say to me its mechanical rather than
electrical and so eliminate spark problems.

Running longer when in gear is a clue, but I don't know why.  I assume
you mean automatic drive 'in gear'.  This would mean there is some load
on the engine, possibly drawing more fuel and keeping the pressure
regulator away from its sudden release point for longer.  However it
seems a highly unlikely failure mechanism to be so time constant.  Maybe
pressure builds up because it is sticky and then suddenly releases
totally because the spring is broken.

A mechanic should be able to test the fuel pressure, but its probably
cheaper to eliminate the regulator by replacement.

Perhaps you could monitor the tank return feed, it could be dry then
suddenly gush just before it stalls as it losses pressure.  I don't know
what would happen if the return feed was blocked, but if you could try
that briefly it might run on.

--
Tony