I'd like to determine whether a particular phylogenetic problem is too large for current parsimony-based methods.

Would anyone happen to know the largest parsimony-based phylogenetic reconstruction that has been successfully completed?

The datasets I have range from 5000-25000 tips, and as far as I can tell these aren't solvable using parsimony, even with heuristic search methods I know of, within a sensible timeframe (even using cluster/super computing).