Specify Custom Shipping Box Size/wt per product

We sell cups,mugs & bottles in bulk, but priced per unit and each type of bulk product is bulk packed in specific size boxes.

Examples:
Box A (20x20x20 @ 13 lbs) fits 45 of our 32 oz mugs.
Box B (24x16x12 @ 33 lbs) fits 100 of our 14 oz mugs.
and so on.

We’d like to specify the max pack count of mugs per box, per product and woo calculate and send the data for a live quote to (UPS or Fed Ex etc)

For instance an order of 200 of the 32 oz mugs, it would take 5 boxes (rounding up from 4.44) with each box sized at 20x20x20 each having a weight of 13 lbs each.

We’d need to set a specific custom box size, box weight and pack count for each product.

We’ve seen many plugins that are close, but none allow for specifying a max quantity per shipping box and allowing the second (or third, etc) box to be calculated. Seems they only limit a max quantity per order/cart, and we don’t want to limit the quantity that can be purchased.

USPS live rates plugin doesnt allow tying a custom box size to a specific product and flat rate table rates doesnt kick back live rates and neither allow to set the pack count per box and have the logic add another box to pull (& then display) a rate quote.

We dont ship via flat rate and native woo doesnt allow input of box dimensions when multiples of the same product are ordered, that would ship in the same box, with limits to how many the box can hold.

Weight based plugins also arent helpful, since our boxes are set by pack count, not weight and that would lead to inaccurate quotes and extra work in us having to calculate the weight of the mugs per box, for all of our items.

Any help is appreciated!