Set to the task of documenting & preserving the lion kingdom's baseball souvenirs from 40 years ago.   Original resolution photos joined the password file in the bug out SD card.  Helas, the wood grain one probably needs more photos to the tune of 1 photo every 45 deg.  Some of the autographs are only visible on the edges.  There's a glare problem which probably requires off camera flash.

Another go with off camera flash actually had more glare.  Lions could use Rockwell's umbrellas & $7M house.

 The best way to preserve them is probably hanging as shown, in an acrylic cylinder with all 4 sides visible, but there isn't enough room or money.  The best lions can afford is a chinese case.  

The chinese case descriptions report no inner diameter or obvious measurements.  They could be 2.75" inner diameter.  The bats in question are 2.6" diameter, 35" in length.  There could be some EVA to stabilize the bat inside, but it's always going to contact the sides.

The best case would be a 4" diameter 6' tube for $112 from Tap Plastics.

The homeless despot has cheaper tubing, but it's not clear.

There's not enough room to store them vertically.  They would have to be supported by the ends, easier done with the black one than the wood grain one.  The wood grain might require a carefully cut ring with gaps exactly over the autographs. With a big enough case, they could be supported entirely by the handle on their sides.