It's a crap shoot!
I have done a few bows like this (frankenstein type bows, not this exact combo). It is an interesting project, and the bows are fun to shoot, but I'm not sure if there is any real advantage. Anywho, you are presently at 38" ATA and about an 8" brace with that Protec, is that about right? The Apex 7 is 37" ATA and a 7" brace, I believe. I would start with a cam that is for 1" shorter draw, due to the brace differences. The ATA is close enough not to change much. If you go with an Apex cam, that is 41" and 8" brace, so maybe get a cam that is for 1/2" longer than what you want. Your limb deflection may be quite different than the Apex limbs and limb configuration. I would guess you might lose some draw weight. You could make that up with a shorter harness and more prestress, but that would also change draw length. You can always buy a different size cam and sell the one you started with if needed. I would think it would take some time to get everything dialed in the way you wanted it. When I do this type of thing, I make my own "temporary strings" until I get what I am after, then make a good set or buy custom strings once I have the length. I guarantee if you ask this question on the Mathews forums, you will be strongly warned that it is not safe to do. You could end up with a pretty cool bow with your idea, but it will take some time and patience to "git r done".