Help Solve a Mystery!

[EF XR8]

Help solve a mystery!
Hi
I have just rejoined the forum after an absence of a few years in the hope that one of the grease monkeys out there can help with a problem that has stumped just about every mechanic in Canberra.
I have a 1995 EF XR 8 with 130 000 kms on the clock. The car was a police car at one stage. It has cruise control that has never worked. The car has a major idling issue that noone can fix. When cold the car will start OK and idle OK for about 30 seconds before starting to idle rough. This continues for the next minute or so, getting progressively worse until the car almost ‘chokes’ itself before suddenly clearing and running fine. If I drive the car in that time without letting it go through the whole process before driving off it is dangerous because it is almost impossible to accelerate beyond 1500-2000 rpm. If I have to accelerate faster than that the car will miss and cough (almost sounds like a muted backfire but in the engine bay itself, not out of the exhaust) before it clears and runs OK. When it ‘clears itself’ it will surge forward, regaining some of the zip that an XR8 should have.
The idling problem happens again as soon as I turn the vehicle off, no matter how warm it is i.e. I could drive it for 3 hours, turn the car off and then back on again and it will immediately go through the whole ‘idling rough’ routine again
I have replaced oxygen sensors, the air intake system, inlet manifold gasket, distributor, exhaust system, have had the computer checked and rechecked, plugs, leads, timing, ignition all done, some of these have been done several times. This idling and surging problem has been with the car for years now and was experienced to a lesser degree by the previous owner. He also replaced the computer, air flow meter, plugs and leads in an effort to address it.
If you have had any experience with this model I would love to hear from you as this is my family vehicle and it is getting too dangerous to use. As I say, many reputable mechanics have had a go at the vehicle and none have cracked it. I’m hoping the Ford Forum can provide some ideas.