You would almost have to specialize to increase exposure to non-neoplastic pathology. By not specializing, you have to be a jack-of-all trades sorts which includes neoplastic pathology. I think your best bets would be:
1) Renal: incorporates clinical presentation and possible associated systemic conditions, transplants, etc. Electron microscopy is a must for medical kidney.
2) Liver: evaluating labs, metabolic syndromes, viral hepatidites, transplants, etc. Clinical info for non-neoplastic liver is crucial.
3) Cardiac: most of cardiac pathology is non-neoplastic.
4) BB/TM: Don't forget about CP fields! Probably the most direct patient care/management field in all of pathology.
Bear in mind, choosing any of these subspecialties will more likely have opportunities pursuing the academic route (with the exception of maybe BB/TM).