Albeit I havent read through all the posts I will just speak from experience. Aperture and shutter speed will be your enemy here. I do a lot of low light shots at mini pony events and a good majority are undercover arena's, which surprisingly are generally very poorly lit especially when you consider such events as Nationals in Tamworth shot under a fully enclosed arena.

So your key goal is to capture the action subjects in nice sharp shots. I mostly shot with a 5d3 but are still using my old and trusty 70-200 L f4 non is which to be honest, although a fantastic lens, is dismall in low light.

You will need to maintain a shutter speed over say 1/800 and no doubt at the widest aperture - you only option really is to use ISO as your shutter speed setting.
I expect you may be looking at ISO of maybe 2500 - 4000 for action but will drop back to maybe 1600 ISO for non action.

I used to shot with a 50D may two yrs back and honestly, struggled to get what I would consider descent noise level shots.

There is no magic spell to fix your delima with the gear you have at hand. You will get some descent shots. try an minimise the movement by such things as reducing the angle you are shooting a moving player at and maybe some panning may help although I never really found this a great success - Tripod where you can also. I used a mono-pod on my 50D at times to assist. Take as much advantage as possible of the lights and avoid to much dark or shadow areas with the subjects as this will only make it hard to reduce noise and increase detail.
It can be done with some success but it is challenging. Having said that, it is also a great exercise in experience for shooting using ISO as a shutter control also.

And most of all, hone your noise reduction skills in post processing as I think you will need them.

There is some element of guess work in my comments as I do not have experience with the 600D but I have a fair grasp on noise and crop sensors being my 400D and 50D past bodies.

Good luck, if nothing else, enjoy the experience and learn from it.
Hope this helps