Ωhm

Yea, from that side view shot, looks upside down. Check out other photo's, you'll see.

Look into your front grille. ↑↓ Make sure it's installed properly. Welcome to CC.

Somebody give me a cheeseburger.

RENIX 4.0L has no Closed Throttle (CT) switch unlike the 2.5L which does. This CT value is learned over time (40 or more key starts). I know TPS is set to ≈17% at CT, but that’s just a starting point. I’m with you, hope this does it for you. Take it.

Keep in mind when EGR solenoid is ON no vacuum is allowed to flow and the EGR valve is OFF.

EGR should have nothing to do with engine idle. I wonder if given time and EGR connected, could ECU learn its way out of this problem. You've done a lot.

Good to see INJ PW ≈5.4ms at idle with warm engine. Idle RPM’s still seems to be hunting (up/down) for smooth idle of ≈750RPM’s. Few things to think about: -slow to respond IAC. REM can show you what it wants the ECU to do, but is IAC moving quickly enough? -slow to respond O2S. LEAN/RICH should switch just short of the speed of light. -leaky/faulty injector(s). When ST drops to 90, ECU will take fuel away. ECU thinks RICH. -try a known good ECU, if possible. I know haha. Looks like you can leave EGR connected unless you can say, yes EGR is the problem.

Before that happens, at idle, can you post up INJ PW and fuel trim values, both ST & LT. Thanks

If 2.5L learned anything from the 4.0L, both being RENIX, I would hope it would be the TPS & MAP way of how to do fuel strategy. 2.5L still had ISA, with build-in Closed Throttle (CT) Switch. 4.0L learned CT.

87 vs 88 electrical manual wise, show ECU pin C200_8 as WOT(87) or PSPS(88). WOT needed to add fuel while PSPS needed to kick idle up (used when in parking lots to prevent stalling). IIRC

You need to determine if your vehicle has a WOT Switch or PSPS Switch?

All photos look good. You didn't jump a tooth or two. Indexing is not your problem.