Air intake temp: That is what a Booster plug does, fools the ECU into thinking temperatures are lower than ambient thus richening the mixture.May just be temporary.....ECU may adapt and switch back to leaner providing the O2 sensor works correctly?
That O2 seemingly stuck on reading rich?If the injectors aren't atomizing the fuel it won't all burn so O2 may get stuck on reading rich.Or if one uses any silicone products on intakes reassembly?Silicone is poisonous to O2 sensors.
Aftermarket injectors as in cheap copies of the Bosch?Highly suspicious,there are plenty of discussions (and tests)about them.DO NOT use them.If one locks up at speed as talked about in some car forum, that will shut fuel to that cylinder and lean it.And as the fuel does cool combustion chambers......no fuel from a locked injector may destroy the affected cylinder rather quickly at speed!
If one wants cheaper,just about any Ford product from the 80s-90s runs the same injectors albeit with a slightly different pintle cap and part number but still and as per my fuel injection specialist the same injectors.In any case my bike did not have any problems running with Ford (Bosch)injectors.Just me not liking anything Ford related so replaced later with BMW OEMs
OP has a fuel pressure gauge! Any pressure bleed down over time with system primed,ignition Off? A specialist would recommend 1/2hr and no bleed down.I go for 1hr and even overnight,plenty of residual pressure left in my tight system the next morning!
One can also remove tank,rail injectors,reattach everything on an outdoor bench, power the pump/open injectors with a 9V battery, or better a pulser,and inspect spray pattern etc.Carefully......at full pressure them injectors will shoot about 8'.
Or a "power balance test". Pulsers are now rather cheap.~5% inbalance on one injector and another one sticky,not flowing to spec and not atomizing and bike was buzzy/vibey at the 4500-5000rpms range.Off to the cleaner/FI specialist and now smooth.And still smooth 20Ks later.
Pulser, cheap and effective:
Pull away test? 5-6th gear rolling at 2000rpms and then crank up the throttle?Worst case scenario with contaminated injectors is the bike will stall so one should be ready to pull the clutch quickly.Other than that with correct fueling/clean injectors it will pull smoothly from 2000rpms and you'll be speeding in a few seconds.
And general running at low gears speeds/rpms? Should be smooth and the surgey feelings that some have at times proclaimed as normal for the Ks and that a booster plug or such was the cure?Not normal my K with the 296 ECU....clean injectors/no vac leaks/balanced TBs does not surge and does not need a booster!
Hall sensor is a possibility but they hardly ever fail on the Ks.And the wires unlike some earlier BMWs are (should be) the upgraded NiChrome?I'll look at my spare later. Mind you I'd pull the cover,someone may have been in there and squeezed the wires and(or)changed the timing? Or reinstall the plate lining up them halfmoon notches as I have seen done.That is 0 degree static lining them up.
And then you could do a sensor signal test with the rig (9V battery/LED) described in Clymer,toss some heat at the sensors and see if that makes it fail as most sensors will fail when hot?
Timing (static) can also be checked with that same battery/Led rig providing one marks the timing plate as I did.
High idle? 1200-1300 at engine temp up there(105), that's too high.Should be at ~1000 give or take a few!High idle on a K is usually vacuum leaks.BTW my replacement TBs had about your milleage or maybe less but came with dried out and cracked manifolds.Cracked just by the clamp so very hard to see unless unclamped and manipulated.
Vacuum leaks are usually shown as an oily residue around the leak but that can take a while to show.Or a blurb of the engine if slightly shutting then applying throttle.Particularily annoying when applying throttle in a curve!
TPS running angle looks OK, 2.6 is within normal idle running but at 1000rpms.Easy to adjust/check with a Voltmeter especially so with TBs off.And it is basically a potentiometer also easy to check the tracks.
Basic setting with TVA(IAC) removed and reading voltage at pin no1 is 0.34V.But I remember changing it up to 0.42v(?) and my bike instantly ran rough.Idle went up and ran like shit so not even a test ride and I quickly put it back to normal.Just as a test someone was proclaiming that doing such a change had fixed his fueling problems. Not so as it turned out later......aftermarket fuel injectors and some adjustable fuel pressure regulator were the problem.
Jean(Sailor) has a good write up about the TPS.I still have the hard copy but my PDF/Word(?) is gone.I hope he and family are OK over there.