Make a sound proof box, put the wheel inside, seal it up, after taking the wheel off and extending the little bit of shaft it was attached to, cut a whole in the box where the axel/shaft is and stick (with super glue) the wheel back on.
Invest in a more epensive, better built (and quiter) G25
or
Turn up your speakers
I would not bother with opening up the wheel to try and scilence it - all you will do is invalidate your warrenty if or when it goes wrong due too too much LFS
Digging this up a bit, but I've found that folding a couple of heavy sweatshirts/hoodies over the main casing can really help to dampen a lot of the gear noise. You can still hear it, of course, but the difference is very noticeable, especially since the sound is no longer reverberating around the room to the same extent. I'm not sure how much the unit relies on ventilation to keep the internals cool, but I thought I'd mention the possibility of overheating to cover my ass .
The DFGT is supposed to be a lot quiter than the DFP, but the Wingman drivers don't fully support the DFGT yet. So it's either quiet (With lack of controls until a driver update) or the trick you did with your DFP.