RPM's drop and then shut off under load

I do want to thank you for your advice. However, that was not the answer so far. No problem with the cat, and no vacuum leaks anywhere.
Here's the latest: I have started the car a number of times and it will run at 1200 rpm's ( I ran it for at least 12 minutes. Completely warmed up), then attempted to run it up to 2,500 rpm's. It would hold there for 14 seconds the first time, then it lost power and would have stalled out completely but I let off of the pedal and the engine resumed at 1200 once again and stayed there. I allowed it to stay there for 20 seconds, then attempted the 2,500 again. This time it stayed at 2,500 for 26 seconds, then again faltered down to idle at 1,200. Again for a third time after a 15 second idle, this time to 3000 rpm's and it stayed there for 16 seconds. No reason for the discrepancies in amount of time it would remain at 2500 or 3000 rpm's. If I remove the pedal it always drops to idle and remains there. Even for another 15 minutes at that idle of 1200. Even if I let it falter all the way to a complete stall I simply wait maybe 3-5 seconds and restart it and all is fine. Until I attempt to get more rpm's out of it. The rpm's can at times fall off incrementally from 2500 (not just all at once), and if I attempt to add more pedal to it to sustain the rpm level it will hold for a bit longer. But with what feels like a bit less power. Almost like I'm losing spark to a plug or two. Not really missing. But running on 5 or 4 cylinders. And working its way down. Just a sense I'm getting. Don't know for sure if that's what's really going on. But just for your analysis?
Since I know nothing about these older carbureted Honda cars I'm wondering if this is an electric and/or sensor related issue to do with some sort of fuel pressure regulating device. What monitors or regulates the speed at which the electric fuel pump does it pumping? It's a brand new OEM pump and I hear it working much like the one I removed, which when hooked up to a power source worked just fine transferring fuel from one container to another). I don't think the original fuel pump actually needed replaced.

I should add that the 1,200 rpm idle that I have it at is due to me setting it there with the idle control adjustment knob on the back of the carburetor. Nothing else has been adjusted. I did however remove the inline fuel filter just before the carburetor (as that was not original. I put it there just to observe the flow of fuel at various times). I removed it to avoid any additional resistance to the proper pressure from the fuel pump. It seems to have made no difference whatsoever. I also attempted my tests with and without the gas cap secured in place, as I noted quite a bit of pressure exit the tank when I removed the cap on a couple of occasions.