If your cruising along at say 3K RPM and nail the throttle, does the engine "surge" or does it "miss".
A surge is when the engine pulls but then flattens out, pulls again then flattens out. A miss is like the ignition key was quickly turned off & then back on again, off and then back on again. Not 100% of time but a surge is generally associated with fuel and a miss is generally associated with ignition.
Since the idle is so unstable I am surprised you have not thrown any codes, especially IAC related.
I filled her up with fresh fuel from a different source...no change.
When the issue is manifesting (sometimes she runs and idles fine, and goes bad randomly), a roll on of the throttle at low rpm results in a cough (seems like backfiring into the air cleaner when it coughs) and drop-out. Going down the road at a steady but fairly low rpm results in occasional drop outs...losing spark or fuel, can't tell which.
I don't know if she has stored any historical codes, but she is not throwing codes to be seen on the odometer.
I have always had a bit of decel popping since the Hooker Tuned flow slip-ons, but only on full decel from relatively high rpm. She has also taken to pop or light backfire (can't tell which) when shifting between 1st and 2nd, when accelerating somewhat.
Steady, higher rpms (say 60+ mph) seem to be much better. I've no symptoms to report under those conditions. But that may be a false positive since I have rotational momentum going for me.
She sounds really confused. My vote is for Glider's 1st suggestion: throttle position sensor, or maybe fuel pump or fuel pressure regulator. I can't tell just yet. The TPS I can replace myself, but don't have the ability to recalibrate. The fuel pump, et al, would likely result in replacement of the whole inside the tank works, since I don't want to have to go back in there.
This is the kind of time when you long for the old days. ECUs and varieties of sensors are a pain to diagnose. Carbs, points, timing and gravity fed fuel were hard enough, but do-able. Now you need adapters and electronic diagnostic equipment...lots of green for DIY'rs.
The only work I have recently done is install a new hydraulic primary chain tensioner, and a Jagg vertical 10-row oil cooler, with offset adapter. In that process, the only thing I could have damaged would be the crank sensor, and I was very careful not to. However I did have to reposition the wires from the crank sensor a few times while installing the offset oil filter adapter. Now I can't get my hands in there to do a wiggle test of the crank sensor's wires.
She was beginning to manifest light symptoms before I started the oil cooler work: rare cough from start when not warmed up, and "sometimes" rough idle when I would stop for traffic lights. I hate when issues seem to correlate, but I guess it would be hard to avoid since I'm doing alot of upgrades to this new machine (to me).
Oh well...one foot in front of the other...
Thanks,
Rich P