Hi. See that you've been here awhile now.
Re sizing. It does sound like you've got a size too big. I am a smidgeon under 6ft with a short torso and found a 56cm road bike too long. As has been said, you could try a stem that is 2cm shorter, this might make it safer and generally easier for braking and control. If not, and if the bike's in good condition, could be worth selling it to someone as a winter bike, ie lots of serious bike hobbyists like to have a bike that's not as posh as their dry weather bike to commute on through the wet and muddy months. And then look to upgrade yourself to say a Triban 3 or Raleigh Airlite (google these).
You might well find the moving parts better on these bikes which will make it less demanding shifting into the right gear for your hills. Chances are the frame and wheels would be better and lighter too. This helps on hills, and, well, generally.
Cheers
Stu