Can you solve this Mate in 16?

It appears that most aspects of the solution work well but there is the nasty dual 6. Kd3.

Thanks for spotting that! A pawn on c2 should do the trick

Looks safe but surprisingly the c2-pawn checkmates in time. After .Kb5 c4+ .Kxc4! white moves his king and bishop to the side and promotes Pc2 followed by checkmate on h8.

Wow! I missed that! 

I haven't checked the diagram below, but I think it solves the problem

Edit: Nevermind, it needs some tweaking.

Edit 2: Perhaps this:

In the last one white can play c5 before the king arrives at d3 because ..c5-c4 is never an option for black anyway. It appears that erecting a proper dam is not all that simple.

In the process you found 2 new checkmate patterns - one with the knight promotion, one with  Nf8#. My personal preference is the last one because all pieces (including wK) on the board cover checkmate squares in at least one of the full length checkmate variants. Even if you can't get the dam to work the new checkmate options are superior to the original challenge.

I underestimated the difficulty of this task! Thanks for catching that!

This might work

Perhaps the diagram below is a better version:

Without the option to play c5, black cannot avoid it. I don't think this affects the main line, though

Edit: Whoops! Still the same problem as Diagram 4 pos. 2 - white can play c4 right away

There are probably several issues. I found that wK can still play to a4 instead of b4 before advancing c4 to c5. The black countermove ...b5+ does not work after .Ka5 b4+ .Kxb4 with some variations.

I think it is safer not to include a wP on d3 in spite of the nice variations where black captures it.

Great find to sac the knight on f2. This is a danger I never considered but looks real!

Still the dam does not look impossible to me. There are many options.