Do some core strength exercises - it'll help all round including on a road bike. You'll end up with aching neck and shoulders if not and that'll most likely transmit to a bad back as you tense up whilst riding. Build up the road miles gradually as you'll be retraining lots of muscles etc to cope with the different position.
I too have a roadrat but with flat bars and that's not particularly harsh IMO but I also run 26c tyres on the pretty stiff 36 spoke handbuilt open pro wheels (use it for off road/cross riding too). The tyres really help for pot hole smoothing.
Also ride a carbon Bianchi 928 T Cube with race geometry which is quite a lot more comfortable than the ali frame/carbon seatstay version it replaced. Neither had sportive geometry so I ride with the stem flipped to point up and as many spacers as will fit under it. I'm just not flexible/supple enough to cope with it in full on hands by the wheel nuts mode.
Handlebars will make a difference too, Bontrager VR bars are shallow drop and short reach with very tight radius bends. This can be more natural feeling than some of the deep anatomic jobbies. That means you are more likely to actually use the drops.
For comparison purposes I used to have a steel road bike and it felt as stiff as the Ali Bianchi albeit heavier.
Cannondale synapse have a very good reputation as being uber comfy - a friend has one and would back that statement up.
I find that tyres make a really surprising difference to comfort too. More expensive ones with higher TPI and kevlar beads etc tending to be more supple and the thinner they get the more pronounced this is due to the higher pressures they need to run at.
So get a cheap bike but budget for decent tyres and maybe a new bar and stem if needed.
