I agree that it would be easier if you had a way to get to the OEM side of the PCM. Since you might not have the equipment for that, I'll recommend some shade-tree methods of at-least getting you pointed in a direction for diagnosis.
The first thing I would do is, listen for your fuel pump priming. Try to see if it sounds weak. Listen to the intake while you're revving the engine, listen for vacuum leaks. REALLY pay attention to how it sounds when it cuts out (Knocks, pings, solenoids if they are loud enough)
If you notice anything odd sounding, check it out.
Once you've done a thorough visual and audible inspection of the vehicle under the conditions it stalls at, its time to actually start testing components.
For this I recommend:
Basic OBDII scan tool (Or better if you have it).
Fuel pressure testing kit.
Compression testing kit.
Intake vacuum gauge kit.
Cylinder leak-down manifold kit. (You need a small air compressor).
NOID light test kit.
Start with your fuel. Throw your gauge and try to make the vehicle stall with it hooked up. If you can, watch the gauge to see if it's movement is stable and up to spec. If you notice that its all over the place or drops heavily under load. You can assume you have a fuel issue.
Test your vacuum. When I say this, you'll need your OBDII to check MAF and MAP sensor data, to ensure they are actually providing the computer with output. If you can safely say they are atleast functioning, use your vacuum gauge to test vacuum.
Your vacuum should be steady at around 16.5mcGH to 22mcGH. This is the sweet spot for vehicles that have proper and steady vacuum. If it falls below that, you likely have an exhaust obstruction or vacuum leak. if its erratic you probably have a gasket leak, weak or improperly installed valve springs / stem seals.
If you rev your engine and it slowly rises up, thats normal. If it randomly drops and comes back up at idle, its most likely a timing issue.
Test your compression, you should have no less than 100PSI on each cylinder (Some can run on lower compression). Measure all of your cylinders dry and with a squirt of oil. They should not differ by anymore than 20 - 25%.
Once you do that, do a cylinder leak down test if you have the means. I'm not going to explain that in depth. Check out a guy on youtube called "EricTheCarGuy" and find his Cylinder leakdown test video. He explains it in depth and very well.
Other things you can do are, pull the plug wires and perform a performance drop test. If you pull your wires one by one and you notice that one of your wires or more does not effect performance when removed, you might have a coil or distributor issue.
I like to pull sensor plugs off while the vehicle is running to see if they make a difference. If you find that you unplug something like a MAF or MAP sensor and the vehicle continues to run normally, you might want to head in that direction.
This is just a brief methodology of how I would do it. Theres a million things you could do.
I would just do this:
1. Recheck everything without disassembling the engine.
2. Run all tests that you can to the best of your ability.
3. Hope you find something.
4. Come back and let us know how it went so we can continue to guide you in another direction.
5. Either redo EVERYTHING you did again and make 100% you did it right, or take it to the dealer and let them deal with it.
I love Suzuki SUV's
Good luck with it!!!!