oh right, you wrote the other 303 web app! I was kinda mad because you stole my thunder while I was working on this one. :)
My Acid Machine app has been built in a way so that all of the instruments are self contained modules, you could possibly create an instrument that would be compatible with the whole UI and step sequencer etc of my app quite easily.
edit: nevermind, I thought you could specify a startTime in addition to endTime but you can't. so you'd have to use audioContext.currentTime to figure out where the sweep should be now, ramp to there, and exponential sweep down to the final value at the end time.