Another possibility is to break it up between 'action' levels and 'puzzle' levels, and players can select either mode.
In action mode, you have all the traps laid out for you, and it's just a matter of timing which traps when to kill everything. Points can be awarded for quick kills, efficient kills, or for completing objectives (kill all the blues without killing the reds). You could make it achievement oriented (get a medal for hitting a target score) or high-score oriented (leaderboards).
Puzzle mode gives the player a complicated setup and limited resources. Level design would be a little trickier for you, since you'd have to come up with puzzles that are difficult without boiling down to guessing the exact places that get you the only win condition. A lemmings-style quota system would give the player options, since you only need to kill 80%, you decide which group to kill, and which to ignore. Limitations could be on number or type of traps, or the amount of times you can trigger a trap before it breaks.
There are a lot of good ways to take this, and they are non necessarily mutually exclusive.
I like the concept of the player directly controlling the castle, manually triggering the traps. I'm not so keen on more tower defense games. I consider that to be a pretty heavily saturated genre.
I really like the idea of a puzzle mode, and think it will definitely be given some thought. The action type mode is what we're giving the most attention now so expect that to be the main thrust of the gameplay.
The quota idea is a good one, but I'm not sure if it would work both visually and gameplay wise. Part of the challenge is stopping the enemies entirely, and once a hero reaches the princess ... he pretty much has her. I can think of a few ways of getting rid of a hero before he reaches her (a trap door that works until the quota is surpassed, spikes that are in place in a similar way) but they might detract from the core gameplay. And higher difficulty in later levels, within reason, might be more fun than more leeway. The player will have to stop a set amount of heroes in each level, though, with early levels having 2 or 3 heroes, and later levels having maybe 15 to 20, with variation. We're still working this out though. I expect there's going to be a decent amount of playtesting to get it right.
I agree, a tower defense game is not our goal here. It's more of a action-puzzle-platformer. There's some tower defense inherent in the gameplay, but only the defense part. The heroes will not have health and the traps will not be automated.
Thanks for the input.