When I was messing with the megasquirt I built the engine would start and run on the start circuit but as soon as I let the key return to the on/run position it would die. It would run as long as the starter was circuit was on, sorta' tough on starters. I was getting no fuel signal except in the start position. I don't know if this has anything to do with your issue.
Do you have fuel pressure gauge? If so hook it up and check fuel pressure at the shrader valve....should be in the 40-50 lb range If it's a lot higher (because of no fuel pressure regulator return line) the injectors may not be opening. I had a similar problem with my son's 37 Chevy after installing a LT1 EFI driveline, one of his buddies bent the return line and the fuel pressure went up to about 90-110lbs PSI..the 24lb injectors injectors could not open under that pressure.Oh yeah...if the MAF sensor is on backwards..it will start and shut off. If your LS harness has an OBD2 connector...try reading codes.
Maybe hook up a noid light to insure the injectors are getting power while cranking, watch the fuel pressure after you prime it and it starts temporarily....to see if it spikes.On a side note just last week my 1994 dually truck with TPI wouldn't keep running...I ohm'd the injectors and located (3) bad ones. Replaced all 8 and the truck runs like a beast again.Have no experience with those self regulated fuel filters....but it seems that there is a fuel issue if everything worked before the swap?
The noid lights are basically test lights that plug into the injector connector. If the injectors are getting a pulse they light up. Harbor Freight sells them:https://www.harborfreight.com/search?q=noid%20lightsAs far as a tune if you have the same PCM it should start and run...a tune would be required to optimize the new intake flow etc. Your current PCM must have had VATS tuned out ? because the condition resembles a VATS problem.If your the new injectors are the same as the old ones (lbs and flow rate)..the old tune should work to get it running. Sounds like if you spray starting fluid into the throttle body it starts? Do you have good spark?
Here's a write up on GM MAP sensors....it has the old style MAP sensors...you are most likely using the newer/smaller sensor?...maybe this info might help ID which BAR sensors you have...if the old and new MAP sensors have different BAR ratings I suspect that will be your problem!https://www.robietherobot.com/storm/mapsensor.htm
10-4...I think have you the problem narrowed down. Maybe some rubber hose/tape to make it fit? If I can help I have a bunch of the old style 1Bar sensors.
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