I actually love this idea for a local multiplayer game. It reminds me a little of Gang Beasts (in which you basically wrestle/punch/kick etc to kill your opponent, whether by throwing them off/into various objects), which I find a blast to play with other people. Sometimes simple mechanics like this can be really fun, if given the right abilities/tools. It can get rather hectic. But, something single screen-multiplayer like along your idea sounds great to me.

Add objects in the terrain which the players use to try to get the other players (or counter things the others are trying to do to them)

Not neccessarily picked up boosts or temporary objects which open different actions.

Also things you strike/push that send them into motion (falling, sliding down, flying up and coming down, etc) including some cascading effects or ones you move a little (to open a climbing path in the terrain - or block one). These things might not deal damage but impede/delay the other players (and things they set in motion)... for a while (AND may disrupt the players own actions if they aren't careful).

These objects then interact with others in a multitude of ways (which might take a while to figure out - and thus a reason to play further to see whan they do in the different combinations). The active behavior of the object should eventually settle again (some varying period for different things).

Possible poured liquids/sand type flows (ones that flow down because of gravity)??

Fires/gas clouds that spread (and dissipate)?

With the other potentially players in motion having obstacle placed in their path (to unexpectedly halt them to be jumped on) will prevent the game from just being an endless chase (with the terrain quickly figured out).

Having the various objects types and counts semi-randomly placed can make each game play different.

I think that it seems as though it could be a fun party game, and there's precedent for a similar type of game in Towerfall/Towerfall Ascension (a gameplay video should be here) and others, I believe.

You say that you feel that you can have an alpha ready in a month; in that case, my main suggestion is to prototype it and see whether it's fun. The initial prototype needn't have anywhere near all of the features of your description: have two players, controlled by opposite sides of the keyboard, a single level, the basic head-stomping mechanic, perhaps some of the navigational mechanics (wall jumping, for example), and maybe one or two items. That way you can try it out, and give it to us to try out, and hopefully get feedback on it.

If I may give one warning, however, it's this: beware feature creep. For a game as simple as this, beware the temptation to keep adding more and more features onto it. By all means add features that significantly add to the experience, but you indicated that you want a game that you can complete quickly, and I suspect that a party game like this might be well-served by being kept fairly straightforward, thus allowing people to sit down and have fun without having to spend much time learning how to play.