I cut a couple pieces off the rearmost crossmember and off the back of the forward crossmember to get my spare raised up underneath. Then, similar to what we did on the 80's as a spare tire lift, I raised it up underneath. I was going to raise it up again since I now have a little more space. Not sure if this will help, but possibly. I can send another photo but I think it will be obvious what I removed when you look.
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Ultimately, the tire must still fit between the those two crossmembers, however if you are just a sliver away from fitting, I would grind just a little off the back of the receiver slot as it protrudes from the crossmember. Maybe another 1/4" without compromising that weld