Spec' Tarmac (road), Spec' Secteur Disc (commuter & tourer), Salsa Mamasita (MTB), CoMo Speedster (tandem), Surly Big Dummy (cargo), Airnimal (folder), a train pass, and NO car :)
In addition to the difference in handlebar diameter, your 105 brifters will not work on a straight bar because the bar has to be curved to give enough room for the brake lever travel. It may be possible to mount your brifters on "Moustache bars", which are flat, but have a sharp bend where the bar sweeps back towards the rider, and this provides a place to mount the levers. I've seen it done before, but I'm not sure about the ergonomics of operating the shifters from that position.
To use straight bars, you're going to need a new set of brake levers (make sure that they're NOT designed for V-brakes, and are instead designed for road calipers / cantilevers) and a set of Shimano R770 trigger shifters.
just sell your shifters, you'll fetch plenty of money for them and flat bar shifters are a lot cheaper, just make sure your careful as sometimes they take a special fd that allows road sized chainrings but pulls at a different ration than a road FD
Try moustache bars... its a less expensive conversion than moving over to an Albatross bar.
I have an Albatross bar on my Lemond Zurich and after getting a Bontrager offset seatpost, the fit is now dialed in the way I like it by moving the saddle forward. This shortened the long top tube and now riding in an upright position is something I now look forward to on it.