Since this is a pipedream (emphasis on 'dream'), and to stay within the confines of the EAA (going towards the warbird/classic aircraft arena), I propose this list to choose from:
Pitcairn Mailwing
Waco YMF or UPF-7 or Taperwing
Great Lakes 2T-1A
Yak 3 or 52
Boeing Stearman PT-17 or 450

But then, I would be happy just just to be at Oshkosh to watch any of them fly. Best to all and good luck in the next sweepstakes