As far as uneven pitch response, I'd say that you probably need to move up in string guage. I use a 60, and I'm tuned to B flat. Maybe a 65 would work. If you tune a string a couple of frets lower than whatever the standard pitch is for that guage, you can see that the shape of the vibration of the string changes. It gets slightly smaller, then larger. That affects the pitch stability. This is particularly true for the open notes.
The lower you tune, the more problems you'll have with intonation. Thicker strings will help, but what you really need is a longer scale length. If you don't have adequate scale, you'll have to compromise your intonation. If you think about it, you're tuning you're low string to the same note as the A string on a standard-tuned bass. Look at the difference in scale length between the two.
Chorus may help you to come closer to the tone that you want, but any professional CD that you listen to has lots of guitar tracks - at least two playing each part.
Don't give up. As you get used to playing in the lower tuning, your technique will adjust to what you're hearing. It gets better.