Kajero, I am also short, and that doesn't necessarily mean you cannot get faster, if that's your goal. But, it sounds like you just want to find a compatable group to ride with. My club has rides at your speed, so others must, too. I'd advise looking at outdoor groups or meet ups, rather than a bike club. I am probably similar to AZ in speed, which means with typical bike groups, you are in the middle.
I hear frustration in your voice. Maybe you should focus on your skills, and that would improve your speed. If you are causing accidents, that's a skill issue. Perhaps not only bike skill lessons, but also core, balance, and strength training.