Megan, you may recall that one the Cleveland P-51 racers had the rad moved out to the wing tips - was it the ill-fated Beguine? - and another modified by Anson Johnson had the rads in the gun/ammo bays I think - it's now on display at Windsor Locks though not when I visited sadly. As far as I know, Galloping Ghost was the only Reno competitor with the dog house removed.
Major modded P-51s at Reno that I can think of were Red Baron, Stiletto, Dago Red, Strega, Voodoo, Sumthin Else and Precious Metal, all of which retained the belly radiator. Miss Candace/Jeannie did too until modified as Galloping Ghost by Jimmy Leewood.