Hiya,
I'm also a redact user shooting on an unmodded Canon 5D MK III. I always do a bit of cropping as 250mm focal length is very wide field in astrophotography terms. Its always worth having a look at tutorials online and watch peoples processes with the same telescope and see what they do, I find that a good starting point of what to shoot. Chances are you're always going to be cropping into an image some what. You've also got a crop sensor on the 650D which I would say helps as well.
For reference this is a cropped in image I got the other day of the Orion Nebula, this was about 25 minutes of integration time. Subs were 90 secs.....I think.