I had this issue with my 4x12 recto cab for a long time too. Using a 50/50 or 2:90 power amp, along with really bassy presets on my old preamps, I was always pushing too much bass, but when I tried to lower the bass it made the presets sound really thin.
The main problem I was running into was that I've come to the conclusion I was running the wrong cab for the amps. Now I'm running a triple rec into the cab, and even cranked up it never woofs like it used to.
So I'd suggest lowering your bass, or getting a 20 or 30 band graphic eq. Keep putting segments of the graphic eq lower until you find the set of frequencies that are making that cab vibrate. Eliminate those alone, you may be able to keep a fairly bassy sound with only losing the cab rattle.
Also, goes without saying, make sure the speakers and the back panel are screwed on fully. A bit of double-stick foam tape between the metal backpanel and the back wall of the cab will deaden the issue too if you had the same problem I did.