Has anybody changed the sequence of a series?

[LilyBLily]

The first book in my six-book series was published over four years ago. I advertise it constantly on Amazon and it's in KU. I don't like its sell-through numbers, and sales and reads have declined this year.

The story itself has some intractable problems that no amount of rewriting can solve and was not written to start a series. I don't repudiate the story, but I wonder if I should reposition it to a later spot in the series, or call it a prequel, or do something else so I can to advertise Book #2 as the series leader instead?

Sell-through from Book #2 to Book #3 is very good and Book #2 is a much better written story, IMO, with a larger potential audience. Also, it doesn't have a purple prose title that attracts the wrong sorts of readers and repels the right sorts. [I can't change the title without buying a new cover (the designer died and there are no files).] There's no number on the book cover and I could change frontmatter and backmatter text as needed in all the books to reposition them. 

How difficult would it be to change the numbering of the series?

[Dormouse]

Finn Bell seems to have done. And changed the names of the books.
They're packaged as a series now, although I don't think they were originally so it's not quite the same thing.
And there only seem to be two books that he's put under the series title.

I find it confusing. I think it would have been easier for him to stick the series title on revised covers and put the second down as a prequel.
Apart from the setting and the fact that the protagonist in the second makes a small appearance in the first, I'm not sure there's is anything connecting them (I've only read the first one).
And I have no idea why he changed the book titles - seems a strange decision since they won prizes under the originals.

My feeling would be to change the first in your series to a prequel. Assuming that works sequence wise.
But not to change the titles.