You could get one of the new Sturmey S3X hubs and build it into a Used frame with track style or horizontal dropouts, to get the chain tension ..
http://www.sjscycles.co.uk/product-S...Hole-22102.htm

the fixie is an engage or not, freewheel, shift, and there is the 3 speed gear select, both ends of a drop bar, so a frame with 2 brakes would be best..

you could get some deep drop track bars of chromoly , and put road brake levers on them ,+ , the bar end shifters .

Match sprints from every stoplight, that should be aggressive enough.