I don't think much on breaking in new tires or sand them down for that matter. I just recently put on the shinko 712, then immediate out for a 100 mikes test ride, just to "rub" the new rubbers, then about another 350 miles or so for Godzilla relay ride with many twisties. Tires handle great since new. I might add that I also ride fairly aggressive on my bike.
+1. This year I have put on a new IRC rear tire on my K4 (while on a trip to the Blue Ridge Parkway, NC where cornering was hard and tight), new rear Bridgestone on my K2, new rear Metzler on my VStrom and in each case rode it normally (hard and fast) straight away with very positive results. I never scrub tires or anything like that. Put them on and go, no break-in required. I think scrubbing tires is an old wifes tale or irrelevant these days.
The tire wanting to go straight sounds like its under-inflated - I got this same feeling when I had my front tire punctures (5 in the last 15 yrs)....slow puncture with air slowly being let out and suddenly you cant corner as well and then...oh-oh...time to stop!! Or maybe the tire is way out of balance (see this with cheap Kendas).
good luck in sorting it out,
cheers
Andy