I'm not thinking that there should be much of a difference between how the 2.8 ran, and how the 3.1 runs. So either I'm wrong, or something changed with the swap.
I'm guessing that you kept the "original" injectors. Just to test, try unplugging the fuel regulator, before you start it. Cap off the hose or fitting that supplies the vacuum. (From memory, I believe it's a "T" fitting that also goes to the MAP sensor.) This will allow full fuel pressure to get to the injectors. If it's running lean, that could possibly help it.
I think I remember scanning it, but I don't remember what the fuel trim looked like. But it's not going to show any fuel trim response in open loop, anyway. The O2 sensor has no effect when the engine is cold. It sits at "midrange", and the ECM plugs in a baseline value. It has to start switching before the ECM goes closed loop and starts responding to it.
Also, in closed loop, it's already mostly warmed up, so it won't require as much fuel.
Something that occurred to me... The 85 V6s had a documented idle issue, especially with the A/C on. I experienced it with my 85 GT, back in the day. Ron Robinson experienced it with his 85 SE.
In Ron's case, the fix was a new ECM. I ended up trading the car before it was fixed.
If you've got a spare (any year V6) ECM with a manual chip, it might be worth a try.
I remember when Ron Scantlin tweaked his 3.4 chip for the infamous hunting idle. Seems like his fix had to do with supply voltages, and how the injectors responded at different values.
Did you also keep the same alternator that was on the 2.8? It might be worth watching the 12v source to the injectors. (If you can get to the connector, it will be either of the pink wires. Or you can measure it at either of the TBI fuses in the fuse block. There is one for each bank. Or at the EGR solenoid, which is fed by one of those fuses.)
If the voltage is going "too high", the ECM could be restricting the injectors pulse. This will cause the engine to slow down, in turn causing the voltage to drop. Then the ECM will try to correct for THAT, by opening the IAC AND pulsing the injectors longer.
It also occurs to me that any dis-continuity between the alternator and the battery (positive OR ground side) might contribute to this. The battery will act like a buffer - or a filter - connected to the alternator. Will help to smooth out voltage spikes and sags. Check your grounds between the engine and the frame, and the battery. There is also a fusible link between the alternator and the terminal strip next to the battery. Might be worth a look. Of course, that doesn't explain why it only does it when cold.
For what it's worth, my 4.9 does the same thing, but only when it's very hot, and I get off the highway with the A/C running, and come to a stop. I still haven't fixed that.
All of this is pure conjecture, though. YMMV.