Gosh, I'm loathe to even use the word, but even Wikipedia has an entry on the bomber mafia, and that entry lists some of the main members.
Anyone who uses the phrase 'Bomber Mafia' should be regarded with great skepticism as they are almost certainly pushing an agenda, and facts are entirely secondary (if not tertiary) for them.
personally believe, and it is my opinion not supported necessarily by documentation, that number 1 is possibly true. I'm not sure if they could go all the way to Schweinfurt, but even the big USAAF study that Greg quotes liberally from makes some comment crews gaining confidence and experience in the existing fighter escorts and extending their range through operational procedures (I don't have the exact quote in front of me, I'm sure the experts here will know immediately).
We can do basic calculations of the P-47's combat radius right here, right now, by using document AN 01-65BC-1A entitled,
Pilot's Flight Operating Instructions for Army Models P-47D -25, -26, -27, -28, -30, and -35 Airplanes dated 25 Jan. 1945, and using its climb and cruise charts. Unfortunately, the cruise charts are only filled out to a limited degree, but there's enough data to make a rudimentary attempt.
91 gallons = amount of fuel consumed climbing to 20,000 feet at a 14,200 lbs gross weight
91 gallons = amount of fuel consumed by fifteen minutes of full MIL and fives minutes WEP
48 gallons = amount of fuel reserve (30 minutes' cruising at maximum range settings at 20,000 feet)
The above adds up to 230 gallons, leaving 140 gallons of the 370 gallon internal capacity for cruising. Column V (Maximum Air Range) shows that the aircraft gets 3.03 air miles per gallon at 20,000 feet (288 mph TAS / 95 gph). Multiplying 140 gallons by 3.03 air miles per gallon equals 424 miles. Divide by two since that distance covers the cruise out and back.
So, on internal fuel only, the later P-47s had a radius of about 212 miles. If the distance covered in the climb is included, along with a few other tweaks, then perhaps that can be increased by another 10 to 20 miles.
The theoretical maximum combat radius is limited by the amount of internal fuel remaining after deducting the fuel used in warm up, take off, and initial climb; the combat fuel allowance; and the 30 minute reserve. Warm up, take off, and initial climb consumed about 33 gallons. Adding that to the combat allowance and reserve yields 172 gallons, leaving 198 of the 370 gallons to cruise back to base. 198 gallons times 3.03 air miles equals 600 miles. So the later P-47s could have a combat radius of up to 600 miles provided you could hang enough external fuel on it. (As it happens, two 150/165 gallon drop tanks would do it — assuming the aircraft had proper pylons, sway braces, and internal plumbing for underwing drop tanks, along with the increased internal fuel capacity.)
If we keep the foregoing numbers the same but reduce the internal fuel to 305 gallons, that lowers the fuel remaining by 65 gallons, which is 195 miles, dropping the theoretical maximum radius to about 405 miles. Of course, that is not really a fair comparison since the earlier P-47 models might have had better cruise performance figures, but it might be illustrative nonetheless. (There is a PFOI available for earlier Thunderbolt models, but its cruise charts are very sparsely filled out. The air miles per gallon in Column IV and V are significantly higher than in the named PFOI, so I am skeptical of the figures' accuracy. At 10,000 feet, it has 3.24 air miles per gallon in Column IV and 3.69 in Column V. For the later P-47 PFOI, it's 2.69 and 3.00 in Column IV and V, respectively.)