I dont understand.
Why compromise the sound of your guitar over a tuner if you like the way the present pickup sounds? Have you tried using a feedback buster (which would block the room noise from the inside of the guitar)?
Also I am with you about the vibration tuners not being accurate enough. The other nite I was using 1 while playing out and about threw the thing, I was so disgusted with it. BUT my suspicion is that it's because mine is a cheaper model. Have you tried 1 of the better ones? I'll bet some are much better than others...... Without a doubt certain tuners are junk. I'm convinced of that now.
All I know is that you may not like the way a different pickup sounds. It's a shame to replace something you like IMO..... You said you LOVE your pickup. I'm sure there's a way to keep it and still be able to get accurate tuning. Try a feedback buster (plug) if you haven't and/ or take a look at all the options offered in tuners first....
Ryan