Time for some closure.
I re-pinned the connector for the MLPS switch using the bottom diagram here:
https://www.oilburners.net/threads/e4od-mlps-wiring.42601/#post-479945, but discovered that this did not match what was needed on the new Motorcraft MLPS (SW5978) switch I purchased for my truck. Long story short, the wiring had to be reversed according to how the diagram has it shown, so Pin #1 and #5 need to swap sides, Pin #2 and #6 swap, etc. all down the connector. I verified this by using a multimeter set to ohms/resistance and probed the different pin pairs while moving the MLPS switch to the different positions and took notes. In the end, the picture below is how I had to wire mine:
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To help determine this, Pins #1 and #4 in the diagram above will only close the circuit when the MLPS is in neutral position. Pins #5 and #8 in the diagram above will be closed in park AND neutral. This is how I figured out on my switch which side my W/PK and R/LB wires needed to go on and then it was easy from there. On a side note, my SIG-RTN wire color on my '89 F250 was colored black with a white stripe, but it still went back to the TECA (verified by checking resistance between the TECA and MLPS). If your truck is a 2WD like mine, then you may not have anything in Pins #1 or #4, or you may have cut wires in the harness for those two spots. From what I was able to gather, these pins/wires are only applicable if you have a push button 4WD. The SW5978 switch also came with a rubber weatherpack that has 6 holes (Pins #1 and #4 are blocked off) instead of the 8 so this would seem to confirm that those pins only apply to 4WD trucks.
Once I installed the new switch and re-pinned the wiring connector, the transmission immediately started shifting correctly and smoothly! I've been driving it for 2 days now and all is well (finally) and for the first time since I've owned the truck the reverse lights now work! My guess is the way I had it wired originally, the TECA could not see which position the gear shifter was in and was not adjusting the line pressure accordingly. In any event, it's driving like it should now and hopefully I can put this 6 month debacle to rest.
So... long story short:
First Round:
New TECA - old one had blown capacitor
New Relay/Socket for TECA - old socket was worn beyond fixing -
Replaced with one of these that works great
Fixed miscellaneous wiring near TECA thanks to finding a rats nest
Replaced solenoid pack and wiring harness for solenoid pack
Second Round:
Rebuilt Transmission
Replaced solenoid wiring harness again (shop that replaced it in First Round broke the locking tab on the harness and did a ****-poor job of splicing it in)
Replaced MLPS sensor and re-wired correctly
Replaced FIPL sensor (could not adjust idle voltage anymore and it was factory original)
Hopefully the info in this thread will help someone in the future. The only thing left is to install a transmission cooler and temperature gauge, but that'll be for another thread. Thanks everyone and have a Merry Christmas!