What are your hokey ideas then?

I'm willing to listen. Dread uses the Jenga tower beautifully to challenge the players manual dexterity. I think it also instills so much tension because the players believe that test is something they can control, sort of like video games where the avatar is moved around the screen to avoid or kill enemies. (I can see them twisting around in their chairs with controllers in hand now) In Timmy terms, I think he would like the game as long as he enjoyed Jenga. There are people, regardless of player typing, who may not like it or have more physical difficulty removing blocks than most.
What ideas do you have for a goal mechanic? I was thinking more self-selected game objectives by the players, which they then share and negotiate in a kind of diplomacy manner to set short or long term team objectives. Diplomacy is an mechanic, I guess, but a "we do it my way" mechanic by, for instance, spending resources would turn me off.
I'm thinking along similar lines. One problem I have is that, in general, I shy away from gamist mechanics unless I can ground them in the setting. Still, one idea I had was to create a pool of drama points that ebbs and flows in the battle. On a player's turn he can specify a dramatic action and use the points in the pool to accomplish it, or he can take an action in order to set up an even more dramatic action and add a point to the drama pool. Ignoring the pool would have no effect, and perhaps changing the dramatic goal would require removing a point. Eventually someone can spend those points to make something big happen. This needn't be part of combat, it could be a tool in intense negotiations. For example, if the PCs know a courtier is having a scandalous affair, in a conversation with king's court they might try and provoke him into incriminating himself. The drama points build as they push his buttons, and then one player can spend them for the final barb that pushes him over the edge.
I was also thinking about some variation of FATE aspects. For example, give the player the ability to temporarily apply an aspect to a creature or situation which he can dramatically exploit at a later time.
Taking inspiration from Dread I would probably not want to use a literal Jenga tower unless there were some weird metaphysical reason that makes sense in the game, but that growing feeling of unease is really powerful. For example, the player can use some resource to gain a more powerful benefit, but each time he does so future uses of that resource have higher risk/reward. If carefully designed into the game there could be a drive to spend this resource as quick as possible in order to end the fight, while holding onto a reserve so that you can more easily block the enemy's empowered actions. I guess that would mean you could spend early to gain a benefit right away, but it will be harder for you to block your enemy's most powerful abilities later. Eventually in this idea the "tower falls" and someone gets screwed.
To go with a more explicitly team-oriented option, perhaps we repurpose the often overlooked "aid another" action or equivalent so that the best effects are achieved only by intricate teamwork. For example, at the start of each round each player proposes the action they would like to take. They can choose to act on their own, but the players are given the option to help one of the other players move toward their dramatic action. This system would probably have a mechanic that replaces the usual initiative system, perhaps by bidding. The most powerful dramatic actions would occur later in the round, so an enemy has greater opportunity to screw it up, but in certain circumstances they might be able to pull off something incredible. If done right this system could beautifully handle situations like extremely complex Mexican standoffs, where the first person to go sets off a chain of events that quickly gets out of hand.
Finally, in a weird twist, perhaps each player would have to specify an action they think an opponent could take against them that would be particularly dramatic. I would want to incentivize the player so they would think of the most over-the-top dramatic thing possible, and then incentivize the opponent to want to try it. I'm not sure how. However, it gives the party a powerful way to influence their opponents actions. For example, a dramatic attack against the fighter might be too good to pass up for an enemy duelist, but leaves him open to the attacks of one of the other PCs. In short, a creature can oblige its enemies to great effect, but that must always be balanced against the fact that now it's doing what, in some sense, they want. (I am flashing back to every kung-fu movie where one of them invites the other to attack.) I'm not sure how this would work mechanically, but I think the concept is cool.
All of these would probably work better in a narrative game. I'm not sure how to smoothly work them in to something crunchier like D&D with combats that usually have tightly defined rules and interactions.