Great question!

Some random thoughts from my brain:

1) You don't have a low enough granny gear! What's your largest cog in the back? Are you riding a double? See my Ode to my 30X27. There is no shame in having a really low granny, esp if you ride in hilly areas a lot.
2) Starting on hills is tough. If the hill is super steep, walk to a flatter spot where you know you can start, clip in, and not splay yourself on the road (speaking from experience here). And even if it's not steep consider your gearing and whether or not you'll be able to start easily enough. If you can't, walk to a flatter spot.
3) Finally, if it were me, I'd walk. That keeps the lactic flush going (still moving, not standing still) and your heart rate will come down.

Just my $0.02.