I think this is a tough situation. I always try to listen to the room from my position and take cues from the band if they want me louder or softer. But what's more important is the type of drums you're bringing in. Not in brand or anything, but in how you tune them. If you're supposed to play softly, but you bring in a Stewart Copeland tuning where everything is high-pitched and cracking, then whatever you do is going to be too loud because you're not in a frequency range that naturally gets blocked by its' surroundings, you're just cutting right through regardless of how soft you play (like piccolos in a marching band that you can hear a mile away). I've done gigs where I've gone in with lower tunings and generally phatter and tubbier (think Don Henley with the Eagles), and I can play my normal volume or a bit more and not be too loud because I'm blending in with the music being played. I don't think audiences are specifically listening to the drums, they're listening for the entire band to be pulsing right along, and reasonable tunings make that happen. You don't need to have your snare cranked all the time. I would think in a cover band situation, you're gonna want phat more than crack anyway, since a majority of pop music is simple time-keeping.
Same thing with cymbals - everyone likes the heavy rides and the medium crashes, and definitely New Beat-type hi-hats, which are cool if you're playing stadiums, but in a small-ish club, those types of cymbals are generally more painful than musical. I've been playing thin crashes and light rides for a while now and the blend and wash is just right. My hi-hats are now 17" thin crashes paired up, and the frequency is so low it doesn't cut straight into your brain, and the cool thing about big hats: you can ride on them! The slosh is musically satisfying.
So I think if the drums are tuned downward, and the cymbals aren't of the slicing variety, you can play your normal volume and everyone will be happy. I remember being younger and only having heavy cymbals and tiny hi-hats, along with higher-pitched drums (I was very much a Copeland disciple then) and when I saw a video, all the wrong sounds were accentuated. It was embarrassing. I still have regular ol' 14" New Beats, and the occasional medium crash, but I hardly use them. Bands like me because I blend in better sonically. This is probably why I like thicker coated Emperors and coated PowerStroke 3's on the bass drum - it all accentuates the low-end, and sounds better when I tune down. Try it.