wing,
Go to 20K in a P-38 and get vis on a 20K Dora. Then chase him as he dives on a 15K bomber formation. Tell me how you do. 
Vink, you couldn't prevent that regardless of what you were flying.... Besides, at 20k the Dora is about 30 mph faster than the P-38J/L.
Could I follow the Dora? Sure, since I'm flying with manual trim, I'd deploy the dive recovery flaps and head on down. The P-38 will begin to shake at Mach .66, and be into full compression not much past Mach .70, but it's controllable. The problem is that the Dora pilot may make one pass and then just skedaddle. The P-38 won't catch him anyway.