Something I suggest is to add another 'crowd' gate half way up your 20' loading alley hinged from the other side for that occasional 'worked up' cow that seems to want to do everything but go in the trailer. 

I would agree you need the 20' to get the cows into the loading alley but I think you'll be surprised at how handy it is have an extra 'crowd' gate to cut this area in half once you have them in there and the first cow or two rattles the trailer to 'sound the alert' to the rest of them.  10' wide is just wide enough for some cows to think they can make an attempt to get by that human critter and if their escape route is cut off by a gate, they are less apt to even try.

One other consideration you might ponder would be a wing fence at a 45+/- degree angle bringing them into the corral.