I know this thread is old but I have a few things I'd like to add. I had the same questions and asked on klr650.net. I was referred to the Frio evaporative cooling stuff. I haven't bought it yet but it is supposed to be pretty good. As you may know now (since you've had diabetes for a while) your insulin does not need to be refrigerated. It has to be kept in a certain range, something like 45 deg F to 80 deg f. If you manage to keep it at room temp. I'd say you'll be fine. I've been diagnosed for about 2 and a half years. My A1C is usually about 6.4. So far it hasn't stopped me from riding, but I haven't done any rides longer then two days either.
By the way, keeping it in one of those small coolers with ice packs works "ok". If you keep it in your top case all day the ice pack heats up pretty fast though. I've also thought about getting some sort of water proof bag that I can put ice in, something small about the size of a small ice pack. That way I can simply stop at a fast food place or gas station and get more ice.