Richard,

It sounds like you have a vellum rather than synthetic head. Possibly it could take a little more tightening but there is always the risk of splitting and they need to be tightened evenly which may be a problem if you have a couple of tensioners missing.

A good man for this sort of thing is Andy Perkins in Faversham. He has a huge range of banjo bits and pieces and certainly could replace a vellum. It's a bit tricky to attach the vellum to the ring if you haven't done it before but easy for someone accustomed to it. A new head, vellum or synthetic, shouldn't cost very much. Another person who can do this is Doug Parry (but I don't have his details any more).

Peace,

Richard (moo)