Over the last few days, I’ve spent what little time I’ve had where I can think a bit more clearly to try and dismantle my old base, bit by bit. I have removed a fair bit of things, moved them into a local storage on a separate beacon, as suggested by a friend and that has helped quite a lot…
However, through those days, I’ve built nothing. And I find this really frustrating.
I haven’t been very well lately, and I wanted to be able to enjoy building something new in Boundless, but for that I really wanted some of the plots from that are being used up at my old base. Instead, I’m tied up in this nightmarish “demolition & removals co.” game that is moving a base with many thousands of plots, plots which I’d really like to just use in my new area, without abandoning all the blocks/items I’ve accrued at the old base!
Not-so-fun-fact: It would take just over 3 hours of non-stop mouse-button-holding to unclaim my base plot by plot, if the “delete beacon” option didn’t exist. Reclaiming all my blocks would still take the same amount of time, however.
In summary, I can’t actually delete my beacon until I’m done removing all the things of value from the plots and I’m feeling quite frustrated about it. 
I wish there was an in-game mechanic to provide a way around such a frustrating situation, such as a moving box which doesn’t let you directly put items into it and only allows you take items out from a previously deleted beacon.