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I shoot a lot of games like these, with such a poor lightning.
I also got the advice to underexpose my pictures, and then bring them back to right exposure with lightroom/photoshop. but when i do that, i have the feeling the noise level just looks the same again. so i do not underexpose annymore.
Now, I tested a lot of programs for post production, and in good light, yea, lightroom and photoshop are wonderfull, for night photography my advice is DXO software. you have there the option for Prime noise reduction. It takes the computer a lot of time to render the image then, but i think it does a wonderfull job. compaired to lightroom, i can boost my ISO almoste 1 stop and get the same result. you can try them for 30 days. If i was you, I would give it a try. Nevertheless The other options you can do with the program i think are better in lightroom.
Okej, i know i used a other camera, but here you can see some pictures where i used prime noise reduction from DXO. schot at ISO 8000 and ISO 16000. (for a 7D it would be something like ISO 3200-4000 and 6400-8000 i guess)