In all honesty, I think you will be happier with a dome lid. The flat lids work but since they are flat, you will have stuff dripping onto the meat at some point.
I am in a similar situation. I have a closed head drum that I have already cut out the lid and grinded the leftovers flush with the lip on the inside. My thought here is that I want to leave the lip on so it will be more rigid. I know that I can cut the lip off and a Weber lid will fit perfectly.
I don't have a lid that will fit right on the outside of the head. I have read that Kingsford lids from the grills at Walmart will fit. I have not checked it out for myself yet but that is the direction that I am going.
Good luck with whatever you decide.
Metro Appliances and More Cooking Team