If wireless isn't an issue, go fondle Logitech's Performance Mouse MX and/or MX Master somewhere.
http://pcpartpicker.com/part/logitech-mouse-910001105
http://pcpartpicker.com/part/logitech-mouse-910004337
They're nice for bigger hands and for palm grip. I have the PMMX and I like it a lot. I'd describe the fit with palm grip as perfect for me.
I don't know how big your hands are nor how to easily describe how big mine are but according to this I'd need US glove size L, M would be too short for the length of my hand where as with width I could use M or L.
Also programmable/mappable buttons. Software allows for presets and those of course include "general button" or keystroke assignments (read ctrl+alt whatever etc) so, should work nicely in games or other 3rd party software if that floats your boat.
The PMMX has the usual back/forward, as well as a "zoom" button and a thumb button.
MX Master has the back/forward, thumb button as well as a vertical scroll wheel. Because of that scroll wheel the back/forward buttons are moved backwards and holding my PMMX in my hand, I couldn't imagine myself liking that.
How often do I need a scroll wheel for my thumb vs. how often I use back/forward buttons... Oh well I digress.
I haven't done any fancy mapping with my PMMX, I just changed the "zoom" button to change DPI presets for normal vs Photoshop-slow-motion. The thumb button defaults to application switcher which is hilariously broken under Win7 + multiple monitors. Haven't thought of any smart use for that button.
The scroll wheel on these is dual function, so basically frictionless/freespin vs steps.
PMMX has a toggleable button to switch between modes.
MX master has a "speed adaptive" scroll wheel so apparently it changes to the frictinless freespin if you go to town on the scroll wheel.
However if "very distinct steps" means you'd like a scroll wheel whose steps and the wheel itself has a higher scroll resistance, then I'd say at least PMMX isn't for you. The steps are in my opinion really distinct but the overall feel of the scroll wheel could be described as effortless.
As for the latency, I can't really notice if there's any. Of course there's the split second lag when you place your hand on it and start moving it, these wireless mice of course go into a sleep state to conserve the battery. It takes that split second for these dumb things to realize they're being moved :D
And at least with the PMMX, it's not an aggressive change of state, well beyond a minute. I'm not gonna bother testing how long it waits before it enters the sleep state.
Battery life? With PMMX, a long time. I don't remember the last time I charged mine and it gets like 10-12h of use everyday. So yeah.. A month, idk.
My PMMX has been whining about critical battery level for couple of days now. Haven't bothered plugging it in.
Another consideration would be that the PMMX uses an AA size NiMh where as the MX Master has an integrated LiPo. Easy to change battery with the PMMX but not so much with the MX Master. Also LiPo's tend to have idk, 100-200 or so cycles where as with normal Eneloops, they do north of 2000 cycles.
Also the LiPo inside the MX Master is 3.7V/500mAh so ~1.85Wh compared to 2.5-3.1Wh for the better NiMH's out there.. MX Master is newer so it's got more efficient internals so battery life should still be about equal if you're looking at out of the box. But you can add roughly 20-25% more battery life to the PMMX simply by changing the included GP Recyko+ 2050mAh for an Eneloop Pro (2450mAh)
Nevertheless, I'd recommend you at least go have a look somewhere, see how they feel in your hand.