So in your example let's say you'd be up against:
3 RHB
3 LHB
3 SH
in fenway or minute maid.
Let's say the three SH are:
C- Victor Martinez
2B- Orlando Hudson
LF- Randy Winn
The three LHB:
DH- Abreu
1B- Helton
3B - Blalock
The three RHB:
RF- Vlad Guerrero
SS- K. Greene
CF- Juan Rivera
-I Know you said the RHB are even and the ones I posted are not quite what you described, but I'm writing off the top of my head now-
In the case above it makes sense IMO to throw a LHP 3R or 4R. Sure you turn the switchers to the BP strength...but towards their weak sides and to the pitcher's strong side.
The reason why I say I consider lineups in the context of BP as opposed to the other way around is because first I like to minimize the number of direct hits If yor throw a L 8R vs. a lineup full of lefties that can hit OK vs LHPs, IMO it is likely the pitcher will get lit even if the BP is tough on lefties...becuse of the direct hits.
If you turn a SH towards the BP strength...but also towrads his W side (as opposed to N) then it's really academic if the BPHR rating is high or low.
But maybe I'm mistaken.