Between losses and bad weather, the 8th Air Force scheduled relatively few deep penetration missions from Dec. 1943 through early March 1944. This is the time period in which the first P-51B units were first introduced to combat, but they were far outnumbered by P-47 units, and roughly matched by P-38 units. (The P-38 could fly deep penetration missions but was hampered at this time by cold cockpits and mechanical bug-a-boos relating to fuel incompatibility.) The P-47D-23 had additional internal fuel, and with better drop tanks had a combat radius of around 750 miles. It's tough making the theoretical arguments about plane availability, because even if a plane could have been available, that doesn't meant that it would have been available and combat-ready in practice. Also, the drop tanks would have had to have been available in quantity to match the planes. Still, it appears that the P-47 could have flown deep penetration missions by April 1944, not long after the Mustangs were available in quantity.
I'm definitely in the camp of people who think the P-51's role in achieving air superiority in Europe was overstated and the P-47's role has been understated. I don't think it would have been fatal to the American bombing campaign to focus on shorter (or night) missions until adequate escorts were available for long-range strikes.
The P-38 (-J) was plagued by much more things than 'British fuel', eg. pilots' piloting technique and engine intake system contributing much to the engine blow-ups.
The 'US Hundred thousands' book gives 600 miles of combat radius for the P-47 carrying 370 + 300 USG (internal + external).