Am I cutting a hole?
On my 67 Barracuda I have a Air Gap with FiTech. The height is the same as a carb. I got a 4'' air cleaner with a dropped base under there after I dropped the base another 3/4". The trick was to use a 16" to get the dropped section out far enough to clear the linkages. I've got about 3/8" hood clearance to the factory pie plate I put on top. It sits so low you can't even see the throttle body. Your issue preventing this might be the float bowls so an oval cleaner might work.