Welp, I went to DokGonzo's and looked at the climb numbers for 190A-5 and 109G-6 against P-47D-11 and P-47N (as kind of a surrogate for a D-11 with a paddle prop and 70" of MAP available.) Pretty close above 20K, Jug becoming superior above 25K. Considering that Johnson's P-47 also gave him a higher level speed, it indeed seems perfectly plausible that no 190 or 109 could get away from him by climbing at typical engaging altitudes during the period in which he flew.
That is not even considering the speculative high-alt performance for the relatively lightweight D-11 with the paddle prop AND hotrodded for 70" MAP.