I find I get the best landings on the 777 by touching down with a slight rate of descent, rather than trying to arrest it completely, the idea being to get the oleo travel used up before the spoilers deploy.
The triple is a very easy machine to 'overflare', in that not a lot happens at 25-30R when the manoeuvre begins, so you instinctively increase the pitch which leads to a low flypast then a sort of flop onto the runway. A better method is to make the initial flare, hold it, then as the wing goes seriously into ground effect the descent rate will almost all come off, leading to a nice touchdown in the right place. The speed's got to be in the ballpark for this to work, though.
I find the 777 very good in crosswinds but if you don't get all the drift off on a dry runway (by whatever method), it will do a sort of shimmying shake on touchdown. This actually feels worse than it is and it's not so noticeable in the cabin.
Coming in faster isn't going to help much, I'd have thought, especially if the autothrottle is in. You still need to touchdown and extra speed will increase the chance of floating down the tarmac unnecessarily.
Landing with one wing (into-wind, preferably) down, even a little, makes for a smoother touchdown. Even better when the auto-speedbrake is U/S and you just deploy them gently after contact.