I have to ask this, because it's been this really stupid phenomenon the past few years where people are referring to (b) flat tuning's as sharp for some dumb reason.
If you are only tuning the guitar down a half step you are in E flat, or Eb, not C# standard...
If you are tuning down your guitar a half step and your low E an additional full step it is Drop D down a half step, not Drop C#
I use to use all sorts of crazy tunings, standard C (that's two full steps down), Drop B (that's That's E flat down two and a half steps for stuff from Sevendust, Chevelle, Red, and Alter Bridge), standard A, and never had problems. However I have always used heavy gauge strings (12's), so that may be a part of it.
I can't speak of an SE because I only own US models that have the Phase 2 tuners, but I keep both of my hollowbody's in Drop C (standard D with the E string tuned down a full step) and they never go out of tune. The CU24 I have tuned down to Drop B for Chevelle stuff and it stays in perfectly. They are all set up with 11 gauge strings.
Here are some video examples of them sounding just fine, no muddiness, no string floppage