I.I. Your pond must be relatively new. Nature will quickly take care of colonizing the finger with water plants. However with nature's common initial introductions (cattails, bullrush, Elodea, narrow-leaf pondweed, eurasian milfoil, chara) the finger will soon become "choked with weeds". The finger could become a "weed" management problem for you; time will tell. Sooner or later you will get most if not all of these, it just takes time. In my opinion keep all cattails OUT. They will start growth along shoreline or in water 2"-3" deep. Pull them. They can quickkly suround the finger and you will not be able to fish through or over them. They can grow 3'-4' deep which is almost all of your finger. Plant water-iris or spike rush in their place. You will like iris better than cattails for the finger in a smaller pond.
Chara you already have. It tends to be moderately good fish cover & forage areas, but it spreads very fast and thus removes nutriets from the water column fairly quickly to fuel the rapid growth (good&bad). As the beds get thick with several years of growth, the mud-water interface gets anoxic, and a thick layer of black septic smelly muck develops under the Chara mat. I think this is very counter productive to a healthy pond. I would try and remove (Lake Rake or Beechcomer rake)as much Chara as feasable as it develops.
If it was my pond in southern OH, I would try to get cork-screw or spiral eelgrass planted in the finger this summer (July-Aug). Some lily pond stores carry it. You are on the northern range for perenial growth of Corkscrew eel grass. It may not even survive winter in your planting-growth zone. C.screw (spiral) eelgrass does not get real tall 10"-14" and it oxygenates the sediments keeping them healthy. Fish can hunt through it pretty well since it does not form tangled masses. It has a slow to moderate rate of spread.
Hybrid water lilies would also be good in the finger but they may over time (6-10yrs) completely cover the finger. Thus only plant the ones you think are prettiest and ones that do not have the largest spreads of 8'-10' unless you want fast coverage. See items in the "search feature" on topics of water lilies for names for names of possible introductions.
