Swapping batteries with different capacities:
it *will* indeed utterly confuse the kernel (and everything
downstream, so notifications, JuicePlotter, etc); unfortunately the
only solution would be to 'reset battery stats' using some custom
recovery rom with that feature. Actually, if I'm not mistaken, it's
just a matter of deleting a file somewhere - but it's probably not
possible when Android is booted, so it'd need a boot into recovery
anyway.
You can try doing this once, immediately after fully charging the
largest capacity battery. *If* it works as I expect, you'll avoid the
annoying low battery notifications with the big battery, but your
phone will die without warning with the little battery (which is not a
good thing in general).
Home screen lagginess:
what you describe is most probably due to low RAM, forcing Android to
reload the home screen. AutoKiller is the solution ;)
JD *does* add some lag at unlock, sometimes noticeably; this is being
addressed with the (soon to be released for testing) v2.x builds
(yay!)