You may have seen my solution already (I can't remember if I've posted it before or not) but it works great. I made a different lid for a wheeled igloo cooler, and it works great.
I made the different lid because it seems like the original lid was hollow, and if I cut it, I'd have to fill it with foam insulation. Also, when I want to use it as a cooler, I just put the original lid back on. I am thinking about making another foam lid for it, for a keg at a party.