Sublist creation, splitting and joining

I have a not very usefully-formatted string list and I would like to create certain sublists from it.

lis = {"F","aa","b","12","c","d","e","2","T","n","1","m","o","3","F","r","s","23","q","0"} 

The desired sublists are to end up containing 5 elements: the flag ("F"), a string produced by joining adjacent alpha elements (if any to join), then a string representation of a number, then another string produced by joining adjacent alpha elements (if any to join), and lastly another string representation of a number. Perhaps easier to visualize as:

res = {{"F","aab","12","cde","2"},{"F","rs","23","q","0"}}

Thanks as always for ideas!