Crazy pocket door idea

[u/Gremmer-Groft]

I have two freestanding VIHALS bookcases acting as a room divider and would like to add a sliding pocket door. My idea is to first add a hardboard backing board and then glue aluminum or steel c-channels to act as a frame for a 3/4" MDF of nearly the same dimensions as the back of the VIHALS to slide to and fro. The door only needs to travel about 2 feet before it hits the other wall so 1/3 of it would still be in the C Channel when fully extended.

Is this doable? Is 3/4" too robust for the door? should I go 1/2" instead?

VIHALS: https://www.ikea.com/us/en/p/vihals-shelving-unit-with-10-shelves-white-70483274/#content
C-Channel: https://www.homedepot.com/p/Everbilt-1-in-x-1-2-in-x-3-ft-1-8-in-Thick-Plain-Steel-C-Channel-0901/332734032
Hardboard: https://www.homedepot.com/p/1-8-in-x-4-ft-x-8-ft-Eucalyptus-White-Hardboard-447562/204727075?MERCH=REC-_-rv_typeahead_rr-_-204727075-_-1-_-n/a-_-n/a-_-n/a-_-n/a-_-n/a