The splines on the axle of the tailpiece are foobered on my 340 manual. Does anybody know if it's possible to remove the tailpiece without taking out the clutch housing?

Which engine? B172 yes, it is, unless one of the bolts has become unpeened, which you won't find out till after it falls into the abiss.

Yes any 340 in fact (although not sure about auto).

Its called the clutchshaft, just remove the driveshaft then unbolt it, should just slide out with the shaft (also a useful centring tool).