"I have a guitar permanently tuned to CGDGCD, I use a .56 gauge 6th string and don't usually have a problem."

Yes, me too. I use 13 to 56 gauge and, after considerable trial and error, have discovered that D'Addarrio are the best for the job on my big Lowden. I have no problem playing without a capo in this tuning but tend to use the 6th string more as a drone to add a bass beat - it's just a question of adapting your playing style and the guitar does need to be set up correctly, though mine still has a very low action. Depending on the song, however, I do often capo up to the 2nd, 3rd or 5th fret (try it on the 9th - the effect is amazing!).