* Long range bomber escort
Probably the P-51D. Not much competition for any side, since no other country was doing long range bombing missions anyway. For whatever reasons, the P-38 was grossly unpopular for most of the USAAF pilots(whether SOME liked it or not), and the P-51D would fly longer and perform better than the P-47D in most aspects.
* High alt interception of unescorted bombers
Ta152H wasn't available until October of 1944, so it can't be a real contendor in June 1944. P-51s or P-47s would certainly have the performance to fly high alt interception, but .50 armament is undesirable for shooting down bombers. So, considering that there would need to be significant numbers in service, wielding proper armament that would do the job, the Fw190A-8 would indeed be the only real choice. Mebbe if the P-51s or P-47s would ever equip 30mms, it'd fare better.
* High alt interception of escorted bombers
Me262, no doubt.
* Anti-shipping missions
Would there be a really serious need for anti-shipping planes in the ETO? I'm not sure about that. Thus, considering the circumstances, I'd say the PTO USN dive bombers would probably among the best.
* Short range dogfight
Spitfires, both the Mk.9 and the Mk.14 would be sufficient.
* Airfield attack
P-38s. No doubt.
* Infantry Support
IL-2. Resilient, tough, well armed, and tank-busting
