If you have 'net access, you can save the page to a floppy or CD, and just have the business center print it off that, which means you won't have to use their net access. Otherwise, you could also go to a place like Kinko's.
If you have a laptop, but don't want to pay for hi-speed internet, you can just use your room phone to get regular dial-up access, as long as you have an 800-number access code to your ISP. That way, you will only have to pay the normal charge for a phone call. (If you don't have 800 access, buy a cheap prepaid calling card and program it into your laptop's dialing sequence.)
Of course, it's not that horrible if you can't do early checkin at MCO, most of the other tourists on the flight won't be able to, either, so the field is fairly level. Just use the kiosks and you will probably be fine.