Altering it so that a player loses when putting two pokemon asleep is not a viable alternative. It is just as "made-up" as the classic clause and is not better in any way.
The currently implemented Sleep Clause promotes a carefree play style that is detrimental to the competitive environment. To prove my point, let me illustrate a hypothetical situation which I'm sure many competitive players have witnessed before:
Your opponent is using Sub Spore Breloom against your Salamence with Fire Blast. Now, your Mence is currently asleep while Breloom is sitting behind his Substitute chipping away with Focus Punch. You have been asleep for 3 turns now, and the chances of you waking up next turn are high. Because of this, though, Breloom starts to spam Spore anticipating your awakening. Now, instead of waking up and using Fire Blast to break the Substitute so that you can finish Breloom off the next turn by outspeeding with Fire Blast again, you are put back to sleep and Breloom is free to set up another Substitute.
Your opponent should not be allowed to spam Spore so carelessly like this in competitive play. If people knew that they could potentially lose the battle by spamming Spore, I doubt they would attempt to do it. This element of play has, until now, been overlooked, and I would argue that it has changed the way this game is played much more than the proposed Sleep Clause ever would. I mean honestly, to devise a strategy that forces your opponent to lose by breaking Sleep Clause would be so incredibly situational, that I doubt we would see any changes whatsoever, aside from more careful play. In fact, the only thing I can see changing at all, is less choiced sleep attacks.
For those of you who have a hard time understanding how incredibly difficult it would be to force someone to break Sleep Clause, let me break it down for you. You have to trap you opponent into staying in, first of all. To do this, you need a Pokemon like Dugtrio, Magnezone, Probopass or Wobbuffet, or a move like Block/Mean Look. Then on top of trapping your opponent, you need to ensure that they will be stuck using a sleep move. To do this, you have to make sure they have a choice item on, or Encore them. In order to get a choice item on, your opponent either has to have it on to begin with, or you have to Trick it on somehow (please note: none of the trapping Pokemon I listed can learn Trick). If you Trick a choice item onto your opponent, they have to choose the sleep inducing move on their own. If not, your plan has failed. If you use Encore, you have to ensure that your opponent will either miss the first time they used the move, or that you have a Lum or Chesto berry equipped. Also, your opponent has to be dumb enough to use a sleep inducing move on a Pokemon that learns Encore and has him trapped. If you somehow manage to do all of this (trap a Pokemon, force it to use a sleep inducing move, and somehow lock it onto that very move), then you will have succeeded in forcing your opponent to break Sleep Clause.
As you can see, a lot of it relies on your opponent not really playing carefully at all with their sleep attacks, and you somehow managing to trap your opponent. This is not a concern to me as a competitive player, and should not be a concern to anyone else who understands how difficult this would be to pull off.
I really hope you will reconsider your opinion of the proposed Sleep Clause change, Aeolus, because I honestly cannot comprehend why it should not be implemented. Especially considering the fact that there will be a pop-up warning preventing people from misclicking their way to a loss, which I think was the only viable argument against this clause.