If you're taking the train, just check in on that side. As others have indicated, check-in on the international side only makes sense if you have transit that drops off directly on the international terminal curb in front of check-in.

Security is generally better at the far end of the terminal, not the center, and the Sky Priority line is usually going faster than PreCheck for most of Monday mornings. Thursdays? You may have better luck.

Does the Cancun flight leave out of E or F?