You know, the least expensive most idiot-proof solution to this is to simply buy a Shimano or SRAM 10-speed MTB cassette, a 9-speed Shimano MTB rear derailleur (Deore or new Alivio), a new shift cable, and a new (uncut) chain. It's not the lightest and it's not cutting edge and it's not going to impress anyone at the coffee shop, but riders who need lower gearing for hills have been doing it successfully for seven or eight years. We can speculate all day about 6800 and 9000, but that's not moving forward with the plan. Or, HTFU a little bit and use an 11-27 or 11-28 road cassette (might need the longer chain, too) with the existing derailleur.
And we can talk about new cranks and bottom brackets and Campagnolo levers, but that does not address the problem as stated in the original post.