For a couple seasons now, I've had experienced coaches request an exhibition game with me, and when accepted, they show up scheduled 3 and 4 days into the future. I've looked at everything I can think of to do that so I can schedule my exhibition games after the freshmen report, but I can't figure out how it's done. Anybody out there that can tell me how to do this?

It schedules the games on the next open day for both of you. The guys you are referencing probably have a game or two already on the schedule so it pushes it to the next open day.
As for scheduling after the freshman sign, the only way to do that is wait until the last day of recruiting and start scheduling your two games with the freshman then. No way to schedule exhibition games in the future.

For instance, in Bryant, recruiting ends Saturday at midnight. So, on Saturday morning, I schedule my final two exhibitions for Sunday and Monday.

I either schedule SIMs or sitemail human opponents to make arrangements ahead of time. The latter can be dicey if the other human coach is also trying to schedule another opponent and they accidentally fill your time slot by accident.

Hadn't thought of the other player's schedule. Thanks for the input fellows.

If recruiting ends on Saturday, for instance, schedule a sim on Friday. This game is played Saturday AM. Then challenge all the teams you might want to play in the next 2 exhibition games. Assuming you get teams to accept, you will get 2 games with the recruits on your roster. Or do as tribewriter suggests, but this way you get a little more lead time for humans to accept. Also, you can challenge humans on Friday and only schedule a sim if you get no takers for the Saturday morning game. I'm not sure how late you can wait to schedule the sim.