Hi Paul,
I must apologize for my lapse in responding, left my I phoneXs on the roof of my Car, just received parts- thank god for Digi-Key for components & AppleGate for Apple parts. Repl.screen, LCD & broken (crushed) S. Mount vertical deflection FET, Cap’s.54$.
Wasn’t pretty...found it a mile away from from where I was. lol.
Clocking the MAF....
Ok...I’m not certain how the new MAF worked out, seemed suspicious but I’ll continue from where we were..
You
can clock your MAF if flanged, in 90 degree increments, better yet I should’ve mentioned there’s an adapter made I usually run, however- if it wasn’t changed, ran right before- i’ll Nix that for now.
Plugs wires and coils.
Uncertain if you had done routine maintenance prior to the anomaly, or a failure reinforced with an abnormal test based on a calibrated instrument as a precursor to replacement, or replaced some typical(s) with new parts, I’ll caution against this if the latter, unconfirmed- I’m guilty, did it before in a pinch, this is why I don’t go to Vegas to gamble. lol!
It may create new issues more often than not. Is advise against ever throwing parts at an issue(Worse, not OE) I’ll guess you had reason, don’t strike me as one of “them”, lol. (I don’t have a money Tree, don’t think you do, if you know one that does, I’m in the market for a good Treeling. I’ll start with a 5$ one, not greedy.. i’ll work my way up

).
If you have old parts swapped out that worked, testing & reinstalling is an idea.
IAT Integration into the MAF.
Your Mustang has the (6) pin MAF and is, in one sensor. Some still split it back off to (2) sensors. It’s a common issue, whether (1) or (2) sensors. As you’re stock in this aspect, if needed, we can take voltage readings from the MAF plug, see if they’re in range, check in parallel while operating, most often occurrence is a wire breakage within, or spray out the connector with electrical contact cleaner, bend the pins slightly, add ‘anti-ox’ to tighten the contact points & decrease high resistance connections.
I’ve also noted routing the MAF harness near Alternator & it’s wiring may cause interference issues As you know already, a very sensitive area.
Low temperature 02 results in a high signal voltage. When the PCM sees a signal voltage higher than 5 volts, throws a P0113. With the manifold exhaust leak you’d had, I’d keep an eye out for that upstream 02. May be slightly damaged, vulnerable (testing an 02 with a VOM on Resistance will destroy it). Best bet is Scantool, watch it.. streaming. If Correcting + to -, good. If it pegs.. not so good.
Cut to the chase...
As your issue is specific to open loop temperature, and the MAF test did what it shouldn’t, as you deduced, I’m thinking
1) MAF
2) The fuel rail pressure transducer.(Data posted).
3) Pump’s check valve not holding pressure for the next cold start.
4) Coolant temperature sensor, a low reading due to air in the System, low coolant.
Or wiring, grounds to all the above.These can all be verified, first.
A quick & handy DX test on both a diaphragm (OBD-1) & combo electrical/Vac (OBD-2) Rail Pressure regulator/Switch, and a returnless F.Pressure sensor, O2 test:
(OBD-2) If an 02 seems lazy watching it’s live Data, try to determine if the sensor is accurately reading the exhaust or not. Remove the fuel pressure regulator vacuum line briefly. The 02 sensor reading should jump rich, reacting to the extra fuel. Reinstall regulator line. Then remove a vacuum supply line from the intake manifold. 02 sensor reading should jump lean, reacting to the unburnt exhaust. If the sensor operates properly, then the sensor may be okay and the problem may be an exhaust leak or vacuum leak unaccounted for by the MAF, Unmetered vacuum leaks at the engine are almost always accompanied by lean codes.
Again, apologize for the delay. Clipped this phone to me now like it’s a pacemaker. Good luck!
Best!
-John