Flying long haul with fridge temperature biologic

Does anyone have any experience flying long haul with their biological that needs to be kept refrigerated? Most airports recommend keeping it in the original packaging, but as I need a few months supply to take with me this means it’s very bulky. The airline say it needs to be small enough for the whole cool bag to be kept in the fridge. Has anyone had issues travelling with their biologic when not in the original box but with the pens individually labelled etc? Thanks!