I have a 94 Ranger with a 6 foot bed and I have put several different 600’s in the bed with no problems. Tailgate won’t close but still had several inches before the back tire was near the top of the tailgate. So I imagine a R3 will fit just fine.
Might be able to put it in diagonally and close the tail gate, regardless shouldn’t be a problem. Back up to a hill and load your bike, there will be plenty of food at the track that will give you a hand loading and unloading it.
Has 2 Ranger, 84 and 97. 84 Ranger had the long bed and a GS500 fit just fine. 97 Ranger was a regular bed and a 99 R6 fit. Tailgate didn't close but used straps to hold it shut.