Nicole,
Kudos for your effort to raise money and awareness for this worthy cause.
Your bike training of riding 500 miles before your trip and only one 62 mile 'metric century' is optimistic at best. Being an Ohio person myself, and having attended Ohio State back in the '70s, there are numerous warm-up rides in Central Ohio in the Spring, quite a few organized Centuries (100 miles) starting in mid March through April and, of course, TOSRV on Mothers' Day weekend - 210 miles in two days, Columbus to Portsmouth and back along SR104. I digress.
You are going to need more saddle time than 'only' 500 miles before setting out on a 3500-mile ride! I suggest you get a bicycle trainer so you can train your cycling muscles indoors all Winter long. Back when I was at OSU I had used old-school rollers. Not only did I get the workout, but balancing on the rollers also teaches a smooth pedaling technique which will make the miles slip by easier. As a cross-country runner, no doubt you have refined your running technique to a fluid motion as well for the same reason!
Anyway, as soon as my budget recovers from this past Christmas, I'd be happy to donate to your cause.
Good luck!
__________________
'75 Fuji S-10S bought new, 52k+ miles and still going!
'84 Univega Gran Tourismo
'84 Univega Viva Sport
'86 Miyata 710
'90 Schwinn Woodlands
Unknown brand MTB of questionable lineage aka 'Mutt Trail Bike'
Plus or minus a few others from time-to-time