Maybe the sidekicks could act as the B-Team, having their own minor side adventures or going off to perform tasks and then regrouping with you periodically. Or they could simply slink off into the background when combat starts, a bit like how Waffles flees and later reappears if things get too hairy. I think there's obvious RP merit to them so I don't think ditching them entirely is the right way to do it.
As for healing, not to push Bird in any particular direction, but if he were to pick one of the various classes where healing is an option (e.g. cleric, bard, druid or paladin) then it wouldn't be as much of a concern.
![Wink ;)](./images/smilies/icon_wink.gif)
Or we could just make healing potion shops more prominent.