Not sure if you could do a whole day in the park. (You’d have to be pretty fit!). The red loop is definitely worth doing, maybe extend the ride into the southdowns/Meon Valley area?
There’s a nice Meon Valley loop which starts at Butser (other side of the A3(M) from QE), then head back to QE for a few more loops? I’ll send you details if you want.
There’s other riding out of the park on the SDW but quite a lot of road to get to the good stuff.
Or there’s all the cheeky stuff, of course, which someone will no doubt come along and tell you about!