Just off top of my head...
Not sure which is the smaller UOM (probably GM) but setup a conversion for the item (EA -> GM, GM ->EA), setup Item Master with smaller UOM (probably GM - may have issues if currently in use and have existing transactions/inventory with EA). When entering the transfer ST order you can enter the quantity in EA unit of measure - I don't think you can do different UOMs like on an SD/OD order. You might be able to setup the secondary UOM for item as EA and then fix display/grid of inventory for sister branch to show the secondary UOM EA (like item availability).
You also won't be able to have two UOMs setup for same item and different branches unless you want to use two different item numbers but then you'd be forced to use adjustments to transfer/move inventory instead of the better method of ST orders.
I'm also not sure if you'd have to turn on the "Dual Unit of Measure Item" in Item Master?? It may be more trouble than it's worth...