I'm pretty obsessive about all of the FD options that Shimano offers and their compatibility, but I'm almost certain that what you're asking for doesn't exist (top pull triple FD that works with STI shifters). Shimano does make a version of the cyclocross-specific CX70 that is top pull (there may be a cheaper CX50 version also), but that is double only.
One option would be to use a top-pull trekking front derailleur operated by a bar-end or down-tube shifter. If you want to stick with the STI shifter, then you'll have to run a regular road FD with some kind of adaptor or pulley.