Sorry to say that if you were to ride your Schwinn hard on PI or PII you will eventually break it. More expensive bikes are made to take the abuse you give it on an actual single track trail. Your Schwinn is fine for ridin' with the kids in the neighboorhood, but no actual off-road riding. I used to work at Roll on Polaris and I would see guys bring in their cheap brand bikes with the frame cracked in two because they tried to take it on Phase I. On the more expensive bikes the welds are stronger, the componentry is better, wheelsets are stronger, brakes are better, shocks are better......This can all be related back to cars.....you get what you pay for. Do you buy the Ebay-no name headers, or do you buy the qualtiy name brand ones.......
I can see where you might get bored, what I usually do is time myself and I wear a heart rate monitor when I ride. I am constantly trying to be my previous time when I go out, which makes for a kick ass workout and and interesting ride. If you can go sub 40 mins on Phase I you're moving....Combo and OMBA are both great websites for local (within and hour or two drive) If you want a challenge, go ride the full trail at Mohican :fuckyeah:
Here are a couple of links with maps, etc.
http://www.combomtb.com/
http://www.singletracks.com/ohio-bike-trails_34.html
http://www.spokejunkies.com/reviews/index_ohio.php
this ^^