I can only memorize about two piano pieces at a time, though neither of them is "Yankee Doodle". The second piece varies (right now it's "Fascinating Rhythm", mostly) but the constant is the second movement of Mozart's Piano Sonata in C Major, K. 545. It's embedded in my finger memory due to a year's worth of practice for a piano recital ages ago. Here is it, played by someone who does it better than I do.
ADDENDUM: Here, for Otepoti, is the version of Fascinating Rhythm in my head (but again, played much better than I could hope to).
My version is up to 1:00. Recording quality ain't great here.
1 hour ago