The current-gen Ultegra crank and BB will fit. A 10sp chain would be best. You know how your chain will begin to graze the side of the big chainring as you shift to your outboard cassette cogs... well, that gets more pronounced when the big ring is 1.5x the size of the small ring, not to mention being spaced for 10sp chains. So a narrower chain will help.

The 12-27 would be a good pick since your goal is easier climbing gears. The final two shifts are three-tooth jumps instead of two-tooth jumps, so your flatland gears will stay the same. Getting a new cassette will also ensure you don't have chain skip due to mismatched wear levels on the chain and cassette.

If the 50 x 12 high gear isn't high enough, you could also opt for an 11-28 cassette, but then you give up your 15-tooth cog, with a 14-16 jump that might be an annoyance.