I'm sure this will come as a huge surprise to you (not) but we apparently have the same feet too. I've got duck feet as well, but mine are smaller than yours (37 - 38 depending on brand).

For cycling, I wear Specialized men's - both MTN and Road versions with carbon soles. The MTN ones are a touch too narrow, but I fasten them loose enough that they work for shorter rides (less than 90 min). My road shoes I wear for longer rides and they have definitely stretched out since I got them. Still, after about 3.5 to 4 hours - my feet ache just like what you described. It's actually gotten worse since I started barefoot running as my feet have spread. My podiatrist has suggested that if it gets any worse, then I should bring my shoes to him and he'll cut them up for me to give me more room (and still allow them to work). I'm not sure how I feel about that but I suppose it's an option.

I also just bought a pair of the Keen cycling sandal in a size too large to use to try 'cutting' to get me more room (I got a deal on SAC). We'll see. I may just have to accept that I can't ride for longer than about 3.5 hours which isn't the end of the world for me in the current state of my life.