Coffee House Puzzles

Over the years puzzles turn up that owe their creation to Coffee House Chess. For example, a joint Lasker-Capablanca problem probably started life as analysis of a coffee house game between the two of them. The position on the right is a much more recent example of the genre, although as a chess 'problem' it is probably no great shakes.
The position in question occurred in a casual game played by two Street Chess kibitzers last Saturday. In the position White decided that he had run out of moves and decided to resign. Recognising a familiar trick in the position I suggested 1.Na1!, as after 1. ... Kxa1 2.Kc1 (or c2) it is Black who has no decent moves and the game will end in a draw. Both players then attempted to try and find something for Black but were unable to do so.
Reconstructing the position on my computer it turns out Black has one good reply. 1. ... Kb1! forces 2.Nc2 Now promoting on a1 is pointless as after 3.Nxa1 Kxa1?? Black loses. Instead Blacks winning move is 2. ... Ng4!! Now it is White who has once again run out of moves, as the trick of Na1 no longer works. Best is now a pawn race with 3.d7 Nxf2+ 4.Ke2 Kxc2 5.d8(Q) a1(q) 6.Kxf2 But sadly for White this ending is just winning for Black.
The main reason for this is the Black pawn on e4. It turns out that if you remove the pawns on f2 and e4 it becomes much more of a challenge for Black to win. So maybe it can be turned into a problem after all.