You are setting yourself up for some misery if you attempt to saturate that cloth in place.
Cut pieces of cloth just big enough to cover one side of the box + 1.5 inches to wrap around each side and splits at the seams where the cloth need to fold around a corner
On a separate piece of cardboard taped flat on top of a table, wet out the cloth with the epoxy with a throw away bristle brush. Work from the center to the edges keeping the weave perpendicular, and use a squeegee to remove the excess.
With both hands peel the cloth off the cardboard and drape in place. Using the squeegee, spread from the middle to the edges. Keep the weave perpindicular. Getting the cloth tight to the wood in the corners with no bubbles is a task. They should be well rounded beforehand.
Some epoxies have secondary bonding issues due to an amine blush. This needs to be scrubbed or sanded off.
Wood can be thirsty and suck the resin from the cloth. Any bare wood should be painted with epoxy and allowed to soak it up before placing saturated cloth on it.
Some people are super sensitive to the hardener used in epoxies. Take all precautions to keep it off your body, and you can use rubbing alcohol to clean the squeegee and gloves for re use.