Here's the thing. You CANNOT take a guitar and tune it down unless you leave it in that tuning and intonate it for that tuning. Also, you've got to make sure the nut is slotted for any string gauge that didn't come stock on the guitar.
The way to properly intonate a drop tuned guitar is to
1. Make sure the nut is slotted for your string gauge, low, but not TOO low.
2. Get the string height exactly where you want it.
3. Adjust the truss rod so the neck is straight, with just a little relief.
4. Drop tune your guitar where you intend to keep it.
5. Use a tuner with a needle, or strobe tuner, and make sure every note on the neck,
especially from the 10th fret to the 19th are ALL dead center on the tuner.
Keep tweaking this until every note is centered.
Now, your guitar is perfectly intonated and should stay in tune just fine. Also, it helps
to do the pinch lock wraparound on the tuning posts, so the strings can't budge.
A little Vaseline, liquid teflon, or liquid graphite in the string slots keeps strings from sticking in the nut. If this is a problem, you really need to have the nut slots cut wider.