Core support question

I have a 1968 dart.
How high does your radiator cap sit higher than your core support?
I have a griffin aluminum supposedly perfect fit radiator, but it seems like it sits kind of high. My hood is still buried in the shed and I’m not really ready to install it yet. I realize that the real answer is probably to put the hood on and close it and check for clearance.
Without the cap on it, just the filler neck alone sits a fat 1-3/4 inch higher than my core support.
I’m not really fond of the idea of cutting the core support and lowering it a little, since I already have a US car tool support welded to the bottom of the original, not to mention they are painted.
I guess though, if that turns out to be the answer, well then that turns out to be the answer.F12CA7AF-987D-4F74-935A-B4FDB1B635A1.jpeg