I wonder how hard it would be to make that L into a big heavy hinge with a heavy removable pin to hold it in place. Of course other tire carriers have that kind of design but they are all but bigger and bulkier than yours.
There is no doubt that adding a hinge and a latch or pin is going to add weight and bulk.
In order for a hitch mounted tire carrier to swing to the side far enough to open the hatch, you would have to have the hinge on the far right or left side. The hinge would be 34" from the hitch. Picture that.
I've never seen a hitch mounted carrier do that. Possible, you bet, a good design,, prolly not..
That function alone would require two, 34" horizontal pieces, which would weigh more than my entire set up. And look awful.
Mounting the tire farther to one side would save some material, possibly expose the license plate and back up camera. With the weight to the side, It would be hard to keep it from failing, due to all the up and down force
Caused by road heaves and dips. Off road, forget it.
Swing out tire carriers are very common on steel Jeep like bumpers. The ball bearing pivot point is on the end of a very strong, heavy, steel bumper. We have plastic there.
If it just drops to the ground when the pin is pulled, then you might want a spring to help lift it. Otherwise, I think it would make more sense to just do what I did. Slide the whole thing out, tire and all.
If you draw your working idea up, any welder can make it a reality. Take your Gold card.