Glad it works out with 1 plot less 
Followng this because I have a similar puzzle to solve for my workshop, my main prestige spot.
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Well, not sure how much help you need, but from what I have gathered, you can become included in a pre-existing settlement if you claimed a plot that is within 2 blocks from a plot claimed by the settlement.
This does not matter vertically. It’s based on the 2-D plain you see when in builder mode. As I could tell from my northern west most point, regardless of elevation, if I claimed a plot within two spaces of the settlement already there, I was incorporated in against my best wishes. This happens because my, in the map, “Orange” beacon is older than the beacon the settlement has near it (in black). So, being older, it can take over blocks from someone else’s reserve area. But, the beacon of the settlement (black) claimed that area before I had expanded my area north in my orange beacon. So there is this strange over-lap, and because of that, all of my 10 beacons got sucked into the pre-existing settlement.
To remove myself from the settlement, I had to unclaim a single plot at that one corner.
Further, I was able to make a guild, and get my 10 beacons all incorporated into a guild settlement/zone. I can change the name of the zone, etc. but I would still be in part of a larger settlement, potentially. It is a compromise, if you are willing to do that.
In short: you have to move, or you have to use guild benefits to form your own little bubble within a settlement.
If you want to move nearby, you could play the slinky game, or worm game, of sorts. You claim a bunch of plots, until you can’t. Then you unclaim a bunch of plots where you are trying to abandon. Claim, unclaim, claim, unclaim. It’s how you keep the AGE of your beacon, while still moving it to a new area. But this only works if you aren’t blocked in, and only within one planet.
I wish you luck with your puzzle.
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