One Clock Simultaneous Check

I thought of a variant of chess. You play 2N games simultaneously against the same opponent. N as white and N as black. You use the same pool of time on your clock for all N games - perhaps 4N hours per player. For example, until anyone makes a move each player will lose N seconds per second corresponding to the N games in which it is their move since they are white. If you run out of time, you lose the whole thing. If you get checkmated on any board, you lose the whole thing. Games do not end because of lack of progress or repetition of moves. Games do end if the player to move has no legal move or neither player has sufficient material to checkmate an unprotected king. If you can not avoid being checkmated, you can refuse to play on that board, but that will  cost you time which you can use on the other boards. If it is understood and agreed that neither player is willing to move, then whoever has more time on the clock per game in which it is their turn to move is the winner since that is what will eventually happen once that amount of time elapses.

It seems to me that playing this well would require skill at tournament paced chess as well as at speed chess and that draws would be extremely rare. 

Has anyone tried something like this?