I frequently make large boxes 12" to 16" high typically gluing up the same day cut. After a few hair raising struggles with standard TB1, I've shifted to TB Extended Time which can be hard to find. Its extended open time gives the confidence needed to assemble, square and clamp. I am most impressed that someone would consider using epoxy since I would think it would create a daunting cleanup job and challenge to final sanding and successful finishing.
Tips I've learned cutting box-joint drawers. Wood species matter. Loosen pattern when shifting from softwood to hard. Glue ... less is best. Easier cleanup and there is so much surface area that not much is required. Drawer/box corners are cross-grained construction. Butts will stand proud in winter and short in summer.
Lee's suggestion is actually what I would do. Cut slivers (hand plane) of the same wood and slide those into the cracks with whatever glue you used. Cut and sand the excess when cured. Since the joints have adjacent end grain you might be able to slide the slivers in on an angle and still have it look right and match expansion/contraction more or less.
"the mechanic that would perfect his work must first sharpen his tools. Confucius