Ok. This is my last shot.
First, you began by describing your R1's steering as "heavy" in relation to your experiences on an R6. Well, provided that your riding style is substantially similar when riding both, no one is going to argue against the fact that an R6 steers much quicker than a stock (i.e. geomety) R1.
Second, when I first picked up my 02 R1, I noticed almost immediately that it steered slower than some of my previous bikes. I noticed this in slower corners, too. However, I lowered the front end by raising the fork tubes in the triple clamps 4mm. Big difference. If you haven't already tried it, give it a whirl. I've heard good results when the fork tubes are raised anywhere between 3-5mm. Also, your choice of tires makes a big difference. My bike's steering quickened significantly when I switched to Metzler M1s. But let's get back to your initial post.
Maybe you're noticing the difference in steering between the R6 and R1 so much in slower corners because that's where you're most aware of the entire steering process. I don't know about you, but I'm more inclined to toss my bike on my knee at 40 mph than 140 mph on the street. If this is the case, you'll be attaining greater lean angles which require more decisive and complete steering inputs. Hence, your greater awareness of the comparatively slower-steering R1.
Aside from that, I'm spent. If you're satisfied with your description of "struggling pushing the bars," I'd be inclined to check for mechanical problems. After all, although the R1 is no R6 in the steering department, it's also no Goldwing either. You shouldn't have to struggle to get an R1 through any turn.
Good luck!