A thought came to me today: Relays can pump a high voltage spike into the cars system when they're turned off. A relay is just a mechanical switch but it uses a coil to create a magnetic field to actuate said switch. When you turn it off it's similar to how the ing coil works; it generates a high voltage spike. Note I said similar, not just like. This is not good for delicate electronics and while I've never had an issue, it can be one. This may explain why your ign box dies on shutdown because you just killed power to some relay(s) that pumped a voltage spike into the system.
So, if you have relays that weren't in there when the car was new, like maybe to control an elec fan or who knows what, it/they may be the cause. It may be that when the ign is on the system as a whole (battery included) can absorb the spike so no harm. If say you hooked said relay to the ignition power circuit so it only works when that's on, now when you turn the key off you just excluded the battery and everything else leaving the ign box alone in a circuit making a voltage spike. A spike looking for a place to go in an isolated system is like a drunk in a bar looking for a fight and everyone clears the room except a 98lb weakling (ign box), which gets punched right in the face. Corny analogy but it was entertaining for me.
Not saying this is it, but certainly a possibility and seems very reasonable to me. So if you have said relays you may want to put diodes across the coil pins of the relays(s). I suggest a Schottky diode because they're faster and will work better than a silicone diode at catching spikes. Just be sure it's rated for a couple hundred volts which I think most are? Then solder it backwards across the coil pins. If soldered fwd you'll just smoke it and/or blow a fuse. The point is the coils voltage spike is reverse polarity so when it fires off the diode is right there acting as a short.
Since we're on the subject, it's possible an oem relay is causing it too. Maybe the spike is getting to the ign when normally it doesn't. I suppose if an ign switch has more than one contact inside it could break the relay circuit a microsecond before the ign? Or maybe whatever oem relay(s) are on a circuit that has a single diode they share but either the diode died or the circuit was moved to that shared by the ign box, or the ign box circuit moved to the relay circuit. Like maybe one or the other circuit stopped working so someone moved it to another spot. Just guessing, but a thought.

Another thought is to simply make or buy a filter for the power to the ign box so it's safe no matter what kind of weird crap is going on elsewhere. Ironically, the filter uses a coil. Basically fight fire with fire. Other weird crap could be something like the coil in the starter is kicking back which would cause it to die the moment you let off the starter which you described. As in maybe the circuit for the starter is connected to the ign, or is somehow bleeding into it. A long shot theory here but if say the spikes only place to go is in the ign switch, which is normally cut off when you release the key. With wear it makes copper and carbon dust, and the key likely has grease for said contacts. Copper and carbon in grease make it conductive enough that a spike just may blaze right through it so the spike that had nowhere to go, now does. Long shot but who knows. So do you try to find whatever gremlin that may be anywhere, or just put a filter on the thing? Or at the very least put a diode on the leads to the ign.

And as mentioned earlier, I'd use external transistors to actuate the ign coil. Option A; have the internal transistor(s) power the external one(s). If you check a now bad ign box and the output transistor(s) are not working the then you could use the pos (or neg) that drives them to instead drive the new external one(s) and save the box. I'd use two transistors because it's easier on the transistor since a coil is a heavy load, at least the coils I've used. Plus if one fails for whatever random reason you're still good to go. I'd assume the factory used two for the same reason?

What you mentioned about the power windows and rpm is a battery thing, so my guess is the new alt is simply charging the batt properly. When the batt is weak it relies more on the alt which is why you see a drop in rpm. If the batt is good it powers the windows with much less voltage drop, it's the voltage drop that triggers the alt to kick in, and how by how much, so the less power the batt had, either old and weak or just low, the more the alt generates and the more it generates the more of a load on the engine.