Watching this one, similar questions.
My son's "96 MGM has so many bad coolant issues we've chased them down to what appears to be a bad head gasket (steam and water out the tail pipe once it's warmed up). It's got around 220,000K miles on it, and the lady I got it from wasn't the most knowledgeable about automotive mechanicals.
It sounds like it'd be easier to jerk the motor, replace the head gaskets, timing chain, water pump, and all the other hard to get to gaskets like the pan gasket, rear main seal, tans pan gasket since it will be out anyhow (the motor looks like it was last cleaned at the assembly plant circa 1996).
I got it for $300, took 7+ hours to drive it 30 miles because the radiator top hose connection was broken at the radiator, so we'd fill it up, drive an exit, pull over, let it sit for 45+ minutes, re-fill it, drive to the next exit, let it sit 45+ minutes .. repeat until home (If the head is warped, that'd be my bad for letting it experience a heating cycle so many times. It only got hot enough to ping once). I also had ProTorque via OBDII showing my the car's vitals.
We put a new radiator in, topped off the coolant and started it (fired right up). Recovery tank was bubbling like mad from the bottom tube w/out the cap. Put the cap on, and it still bubbled but slowed as it built pressure, then went empty (until you loosened the cap, then it'd fill up, and boil). Also the aluminum thermostat housing is leaking where it bolts to the intake (doesn't look like there's a gasket, and it looks like a new intake, with the aluminum front part -and it is cleaner than the rest of the motor- ).
Been searching a LOT about changing head gaskets on the 4.6 (I've built many FoMoCo motors, but no overhead cam motors). The majority of the info is for the F150, and there's a LOT of room to work on it in there. So if the heads are warped, or bad, I think this car might go to where Panther's go to be recycled (pick-n-pull). The motor's drinking problem is the only issue I can see with this car, it is in WAY nicer shape than my 82K mile "05 CVLX was when I bought it for $4000+.
2005 Crown Vic LX
T45 Manual Swapped ADTR Kit
(T45 from a 2000 SVT Mustang)
4:10 Ford Performance Rear Gears
Mo's Speed Shop Tune
ADTR Sway Bars Front
Moog End Links
Moog Left and Right Upper Control Arms/Ball Joints
KYB Rear Shocks (555603 Gas-a-Just)
Moog CC865 Rear Springs (Bout to change to Moog CC501)
Moog Rubber Bits all around
CHE Performance Upper/Lower Control Arms
& Watts Link
E-Bay front struts & springs