I play a Fender precision in an old school rock and roll band, the last strings I bought were 45-105. So far so good. However, I have now also joined a doom metal band which tunes down to dropped C (i.e. the bottom string down to A#). Using my existing strings the bottom String JUST BARELY manages the A#. I can't afford a second quality bass and wouldn't want to gig with a cheap one when I have a Fender sitting at home - so I want to use the one guitar with both tunings. Would going a little heavier (say 110) satisfy both tunings without causing problems at the nut?