My money is on that other goofy thing on the 13B-T... the vacuum actuated shut-off valve.
Try pulling off the vacuum lines going to that flapper valve (it's just above the glow screen on the intake). That will allow the shut down flapper valve to stay open (and prevent you from shutting off the engine with the key) but it will help your diagnose whether you have a leaky or defunct vacuum shut down valve.
Theory of operation... When it is time to shut off the 13B-T, A vacuum solenoid (located under the intake) opens, allowing application of vacuum to actuate the shut down air intake flapper valve, closing off air to the engine, and shutting off the engine. The vacuum solenoid has at least 3 conditions when it will try to shut off the engine - turn ignition key off, low oil pressure, and low manifold intake pressure (presumably because your intake just went underwater... the engine will shut down to prevent hydrolocking, which is good - but if you have dirty air filter, this will also trigger as you are approaching max RPM when trying to merge onto the freeway, which is bad. )
If the solenoid has failed 'open' or some other electrical failure is keeping it open, it will shut down your engine as soon as enough vacuum is built up to trigger the shut down valve, after a few seconds (which matches your problem description)
If the solenoid has failed closed, or you have a vacuum leak in your system, it will be impossible to shut off the engine with the key (this is clearly not your problem, but I share for general knowledge )