You'll have to get the C-2s close. I hate mics close to my guitar because for one it will pick up and amplify noise that we don't normally hear in live guitar performance. But two, having a mic and mic stand inhibits motion of the performer. You might try getting some Shadow SH 711 Universal Transducers. I have the older version of these and they work well in live performance.
Another option, if the space is relatively quiet, is to use a pair of Audix M5050 overhead. Those probably won't solve your feedback problem. If your school cafeteria is like ones I have played in, there is a lot of building noise, so the Shadow mics or acoustic/electric classicals might be the answer.