You have a very normal "bottom pull" cable arrangement. The "top pull" cabling you describe is typically used on MTB and Cyclocross bikes to get the cables away from dirt and impact damage but is almost never seen on road bikes.
Try any of the current Shimano road triple front derailleurs which should solve your problem unless your new bottom bracket is much too long. Does the granny ring clear the chainstay with a big gap? If so, a shorter bb may solve your problem too.