Folks, I don't think we're talking about any weight increase.
Eight M2 .50's weigh in at 510.4 lbs.
Six Hispano Mk. V 20mm's weigh in at 554.4lbs. (I chose the Mk. V because it would have been later in the war after the P-47 assumed the air to ground role where six 20's would come in handy. If anyone prefers that I use the Mk. II 20mm instead, just add another 150lbs total weight for all six guns.)
The P-47 was designed to carry 425 rounds per gun of .50 cal ammo.
The projectile weight of the 20mm is just under three times that of the .50. If we assume the entire catridge weight of the 20mm is three times the entire cartidge weight of the .50, a 175 round 20mm load would weigh the same as 525 .50 rounds.
That ammunition weight x 6 guns would be equivalent to 3,150 .50 rounds.
With a full ammo load, a P-47 is already carrying the weight of 3,400 .50 rounds.
The point here is that the extra 45 pounds of gun that six Mk V 20mm's would have over eight .50's would be pretty well offset by the reduced weight of the total ammunition load because the 20mm cannon ammunition weight at 175 rounds for six guns would be less than the total ammunition weight of 425 .50 cal rounds for eight guns.
This would represent no detriment to the performance of the P-47.
Now even if they were to add 50 more pounds of steel to strengthen each wing, that would cause a negligible decrease in performance.
Now, if you are really concerned about the small weight increase, you could reduce the 20mm ammo load to 150 rounds per gun (like any other aircraft carrying 20mm's) thereby reducing the ammunition weight to that equivalent to 2,700 .50 cal rounds. Again, the P-47 is already set up to carry the weight of 3,400 .50 cal guns. Now, even adding an extra 100 pounds of steel (on top of the 100 pounds we already added) to the wings would still leave you with an airplane lighter than a P-47 with a full load of eight .50's.
For the foregoing reasons, I say the P-47 would have maintained its air to air performance as well.