some further thorts...
1. Thinking that BMW will step up to the plate on bikes now some 16+ years old is futile. If they were ever going to, it would have been done by now. They have little to lose, and no upside when a few cranky old futs gripe about how their far-off-warranty machines work. I'm one of those.
2. If anyone is going to gripe about fuel quality, they're likely chasing a moving target. Fuel age? I've used 7-year old fuel from a resto project a friend did. He had a full tank sitting for SEVEN YEARS in his garage; I being the cheapskate that I am, could not let him simply dispose of it (what could he have done?). I ran some first in my lawnmower, without issues; then in my bike, again without issues. That seven years of storage was in average humidity of 70-plus percent.
3. Back in the 80s, BMW and other car makers ran into problems with fuel condensing in a gummy mess on the back and stems of intake valves. BMW tried a number of things and physical deposit removal via walnut shell blasting seemed to cure the issues - temporarily. It turned out that changing EPA regulations had altered the composition of fuel sold nationwide, leading to deposit issues. In response and after several years of poor consumer experiences, a new federal regulation required a certain minimum detergent additive level in fuels. BMW (and others, including Toyota) found the detergent level insufficient and formulated among themselves a new fuel standard, which came to be known as Top Tier, having FIVE TIMES the federally mandated detergent content. That seemed to solve the problems of the 80s. (That direct injection engines are now/again experiencing somewhat similar problems is a different matter I'll not go into). SOOOOOOO.... if you can, find out whether your local fuel supplier is giving you Top Tier gas. Here in Hawaii, it's all Top Tier, yet we (I) still have stalling issues. I've learned not to let the throttle go to rest at stops if the engine is past the high-idle warmup mode.
4. I got one of the O2 sensor signal manipulators that makes the ECU think it's 20 degrees colder, thus supposedly richening the mixture. As pointed out above, the ECU soon "learns" of this and the device has been of little use. The AX-FIED or whatever, which unit I don't have, may be better, it certainly should be for the greater cost.
Some say a little knowledge is a dangerous thing. There's "knowledge" floating about in reference to the hot stall issue, but no one seems to have reliably solved it, suggesting that either a) the problem has multiple causes and no one has correctly all of them, or b) some can sort the most pressing issue, leading to a subjectively better experience, but see a).