You can actually use more Mouse Buttons by setting them up individually as heal keys. Set them to "pressed OR released" and have two steps. Step 1 = Target Companion/Party Member Companion, Step 2 = the heal. Then activate these keys only while mousing over the Click Bars and deactivate them on 'mouseout'.
This allows you to use those Mouse Buttons as usual while not mousing over the Click Bars (toggle autorun with Mouse4 for example etc).

I personally use my Click Healing setup to heal using my Party Frames and then use two Click Bars next to those for companions when dual-boxing. And since I don't like involving keypresses at all (like the modifiers) I only heal with my mouse and thus use the method above to access more Mouse Buttons. Works great.