Hi Konrad.
This is one area where I've been trying to improve my mixes too. However while you're obviously an acoustic guy and I'm more electronic, I am however very familiar with what a piano should sound like (as I learnt to play on one) and also how it should be recorded so in my productions, I always try to get the piano as natural sounding as it can be but you're right in that standards are so high now and the public have become accustomed to hearing music and vocals which have been doctored beyond natural sounding and any deviation (or truer natural sounding), sounds weird to them so I understand - I think???
Anyway, here's my humble suggestion and what I've been doing as an engineer also told me to carve out space in my mixes.
Firstly I now put Voxengo SPAN on the master channel of every project so that I can analyse each track's frequency spectrum by soloing it.
Secondly, in terms of ducking the bass where needed, I'll use about a -3db reduction and to avoid the colouration that most compressors add, I use the Sonitus Gate in Sonar as this can be side-chained and works really well as you can see the attack and decay of the gate in operation as a waveform so achieving what you need is even easier. It also adds no artefacts to the sound and on that basis, I think it's a fantastic tool!
Thirdly, I've been looking at kick drums in other productions and I've noticed a few things. Some producers seem to tune their kick drums to the root note of the song whereas others leave it alone. I personally can't be bothered with that level of detail as I've also found that it is here where you can get a phase cancellation or even one sound mud-out the other! Therefore, what I've found works really well is to tune the kick so that it sits away from the bass notes and this enabled me to get a kick with more low-end weight as I can see exactly where to locate it as SPAN will show you the gaps in the frequency spectrum as you just can't rely on placement by using a "note to frequency" conversion because of harmonics. I've noted that producers who do tune their kicks to the root note, often resort to ducking the bass or even ensuring that the bass and kick are offset in time so that they don't clash!
Fourthly, then there's the high-end of the kick, the tap or smack of the skin as opposed to the thump and again I've analysed a number of productions and some use a mid-frequency tap for this whereas others use a high-frequency click to cut through the mix. Again SPAN can show you where the peaks are in the kick so you can always put a slight +1 to 2 db push on that frequency just so it cuts through the mix.
Mostly, as I do electronica these days, I create my own kick as I find it quicker and easier than running through a load of presets and finding that later, it get's lost in the mix and I have to trawl through a load of presets again! This way I know exactly what to alter to get my kick punch through the mix. Saying that, I don't like a big top-end click on my kick so I normally have it much more subtle but that's personal preference.
Good luck and hopefully something in my post may help and sorry if I've told you how to suck eggs.
Cheers, Rick.