The answer is simple. Take control of the light using creative flash techniques and shoot at low ISOs (preferably 100 - 400). This will help with noise and might allow you to use a faster shutter speed. There are some really good wireless flash triggers available and off brand used flashes are also very cheap. And these skills will be transferable to the 5Diii when you get one of those. (I've heard that the 5Dii doesn't even have a flash - what a piece of junk!)
If flash isn't an option, consider a tripod (or some other way of bracing the camera). You can use a lower ISO, but, if shooting action photos, a slow shutter speed probably isn't what you are looking for.
You could embrace the noise and turn a perceived weakness into a strength. Have you tried converting to B & W and using a film grain simulator? Sometimes, the results are great.
But ultimately, I wouldn't get too worried about it. In a side by side comparison, a 5Dii might be better, but in the real world, if you've got all the components to a successful photo working for you, few people will care what camera it is taken with.