Oh, seems you already found the one I mentioned.
Honestly, the only thing that happens in the alternate ending is that you get a constellation at the beginning after you beat it.
I could tell you what the alternate ending "involves", but I'm not sure whether to do it here on the thread or in a PM, since it's technically a spoiler (although really not much of one).

Suit yourself.
*puts away the truffles, fluffy pillow, and hot chocolate*

OK, instead of wasting more time here I'm going back to watch grass grow... er, cloud move.

Have fun!

What? You just stand in place in order to get something?

You stand on an *extremely* slow moving platform till it takes you to it.

Wow.

Could someone tell me this: once you do get the star, do you have to complete the level, or can you just use the menu to immediately exit to the cloud?

*Incoherent Laughter*

I believe you can just exit, if I remember correctly. Same as the puzzle pieces.
Or you can just, y'know, lie down on the ground and weep bitterly at the anguish of having to collect the dang thing. That works, too.

Or, if you're like me and haven't bought the game, take the game off your wishlist because of this. (I haven't done it *yet*, but I think I am going to.)

Or stop acting that way as the stars are optional. You don't need them to get the rwgular ending.

It still feels like sloppy game design to have a permanent missible in a game, and is enough of a reason to remove a game that isn't in my primary genre (Braid isn't a turn based RPG) from my wishlist.

(Also, what's a "rwgular" ending?)

A rwgular ending is what you get when you type regular ending on your phone.