Another thread I just read (title starts: "Three 2-minute burts....") that refers to a study where riding all out for 30 seconds, cruising easily for 4 minutes, and repeating 3 more times - doing this 3 days a week - does as much good as riding for two hours three days a week at a moderate pace.
You could fit this in your time range and since you will be able to shower afterwards, it shouldn't be as big a deal working up a sweat.
Of course, you might want to consider your setup. Since you will be stationary, you will sweat like a pig so I guess you'll want a good fan or something to help.
Anyway, it sounded interesting.