Slow speed handling, and I mean reallllly slow speed handling, is key to fighting against 109s for P-47s or P-51s.
The 109s are competent and responsive enough to fight at low speeds, making a very tough opponent even for La-7s or Yak-9Us.. but once it gets down to really low speeds, around 150mph, there's practically no difference between a G-10 and a P-47D.
Turning advantage almost disappears, acceleration as a means of escape, is neutralized, climb advantage becomes very hard to utilize, and the torque factor slowly becmes overwhelming. I've had some fantastic fights with great P-47D pilots in the G-10 at those low speed handling contests.
Usually what happens is, when the Bf109 pilot becomes smug and confident about his handling advantage, he fearlessly steps up to the rolling scissors challenge - which he quickly finds that he can get advantageous positioning, but however, getting a firing solution trickier than expected.
The fight is quickly brought down to treetop levels, and degrades into series of continuous flips, 180 rolls, scissors, and near-stall maneuvering. And at this situation, the P-47 is not such a slouch as expected. The 109 holds advantage in acceleration and slightly better turning. The P-47D holds advantage in less wobbliness, more stable roll, better flap usage and firepower. The two important advantages the 109 holds, is about the same as the three~four minor advantages the P-47 holds.
So the fight becomes a contest of "who drives the plane slower, while turning harder, and rolling more often, and does not stall out first" Firing opportunitys are very rare for both opponents, and it becomes very breath taking.
So, if there is absolutley no escape for the P-47, then the Jug might as well try to lure the 109 into serious of rolls and rolling scissors.