Alright, you're not following me, I can see that.
You wouldn't need a single L bracket at all, in fact, it would be a waste of money to even throw them in there.
You would be buying a larger-than-the-opening 2x-whatever, with the "whatever measurement being trimmed in order to fit it into the opening, and then screwing into that from either the top or the bottom to hold it into place.
The way I'm describing it, the 2x would be touching both the top and the bottom of the opening, one on each side, giving you strength and support on BOTH the top and the bottom, and also keeping it from tipping either back or forward. Done properly, screws might not even be necessary, and it'd STILL work.
Your skis laid flat idea, unless your CP base opening is exactly the height of the shorter dimension of a 2x, won't be as sturdy and will allow your CP to rock backwards a touch. Maybe sturdy enough for your purposes, in which case it will work perfectly.
I don't know what I'm missing in my explanation of my idea, but my idea is strength by physics, not with L-brackets. Hopefully your idea worked. Let us know what you did so we can learn from you.