As you surmise, your shifters will not fit flat bars so along with new bars and probably a new stem you will need "flat bar road levers/shifters" Shimano does make them but i don't know if they are available in 8-speed form. This conversion is possible but could be quite costly. A couple of lower cost options are shown below.

Rivendell offers "Moustache" bars that do take road levers and they are one alternative and while brifters will work they will be horizontal so the shifting motion will be a bit strange. Here is the link: http://www.rivbike.com/product-p/hb3.htm

Riv also offers a modified bend drop bar you may prefer to your current ones: http://www.rivbike.com/product-p/hb1.htm

Both of these bars require a 26.0 mm handlebar clamp diameter so you will need a different stem if you bike has the now common 31.8 mm clamp.