The compact (assuming 50/34T chainrings) with a 27T cog gives a 34 gear-inch low gear. A 34T cog with your current 39T chainring gives a 31 gear-inch low gear. Based on what I've read about the Mt. Washington hill climb neither is low enough unless you are a Cat 1 or better rider.
Others who have ridden the climb say a 27 gear-inch low is an absolute highest low gear they would consider and lower, a lot lower, is better. I've heard of MTB cranks (42/32/22T chainrings) and a Xx32 or 34T cassette being used and they used the lowest gear they had. It's not just the incline, the wind can be ferocious too and that makes the hill far worse.
I see you are from my area. What gearing would you want to use to ride Sycamore St, Realto St. or Potomic Ave. into a stiff headwind if they were over seven miles long?