Just as a follow-up to this, I was restringing the LP again last night (been messing around a lot in anticipation of BKPing and other tweaks :)) and observed that the tuning key on the G-string machine head actually wobbles when there's no string tension holding it firm. That can't be good!
I think that one, at least, needs replacing -- easiest to do them all at once!
PS - the strings I loaded were my last set of Zakk Boomers, but I think that .60 low string is still bit over-the-top. Probably'll take it back a notch to the GHS TNT .10-.52s.