wobble your way to success
Every time you wobble and make a correction, you are learning to steer, sort of. If, hypothetically, you were able to keep the unicycle riding completely straight (for example, by lowering the tire pressure), that might inhibit your acquisition of left-right steering. The fact that you’re able to nevertheless ride 5-7 rotations, while at the same time wobbling, sounds like a good thing.
So, you are making a correction when you wobble, or else you would immediately veer off to the left or right and UPD without making the 5-7 rotations. With practice, this correction will happen more immediately and without conscious deliberation. This will keep you riding straight. The key is practice.
Putting more weight on the saddle is good advice, but I don’t think it can be necessarily rushed. We are not accustomed to balancing on our butts, but we are accustomed to balancing on our feet while standing. Later on, you will find yourself resting more on the seat. My advice: Err on the side of maintaining connection between your pedals and feet; you will avoid ugly falls this way.
You might try to raise the seat a teeny tiny bit, very incrementally. I guess the theory is that having the seat wedged between your butt cheeks (sorry for the visual) helps to stabilize the uni in a left-right direction. My own evolution involved getting the seat up higher, but it happened incrementally.
Sounds like you have some nice neighbors! My neighbors responded differently when I began. To put a positive spin on it, they were probably aware that I’m somewhat of a kook, and that their opinion of me unicycling wasn’t going to change my motivation. So, I got a lot of comments regarding how awkward I looked and a lot of oblique references to falling, as well as remarks related to the “family jewels”.
My story has a kind of happy ending. Many of the neighbors, later on, remarked about how impressed they were at how well I was riding and how much I had improved. Some of these people were the same neighbors who’d made the snide, dismissive remarks when I was learning.
Still, I wish I had your neighbors!