I haven't seen any of these interpretation polls with a good random sample, as opposed to niche meetings.

One of the commenters below the Carroll blog post you linked suggests that poll was from a meeting organized by a Copenhagen proponent:

I think that one of the main things I learned from this poll is that if you conduct a poll at a conference organized by Zeilinger then Copenhagen will come out top, whereas if you conduct a poll at a conference organized by Tegmark then many worlds will come out top. Is this a surprise to anyone?

The Tegmark "Everett@50" (even more obvious bias there, but this one allowed a "none of the above/undecided" option which was very popular) conference results are discussed in this paper:

Which interpretation of quantum mechanics is closest to your own?

2 Copenhagen or consistent histories (including postulate of explicit collapse)

5 Modified dynamics (Schrdinger equation modified to give explicit collapse)

19 Many worlds/consistent histories (no collapse)

2 Bohm

1.5 Modal

22.5 None of the above/undecided

1. Do you feel comfortable saying that Everettian parallel uni- verses are as real as our universe? (14 Yes/26 No/8 Undecided)

A 1997 workshop:

Interpretation Votes

Copenhagen 13

Many Worlds 8

Bohm 4

Consistent Histories 4

Modified dynamics (GRW/DRM) 1

None of the above/undecided 18

More polls are cited at Wikipedia.

A 2005 poll of fewer than 40 students and researchers taken after a course on the Interpretation of Quantum Mechanics at the Institute for Quantum Computing University of Waterloo found "Many Worlds (and decoherence)" to be the least favored

And there is a strange one, for which I don't yet have a link to the original, critiqued at Wikipedia and discussed here, that claimed majority support for MWI in a a sample of 72. The argument for it being compatible with other polls is that it includes a lot of cosmologists, who tend to support MWI (it makes it easier to explain the evolution of the universe as a whole, and perhaps they are more open to a vast universe extending beyond our vision), but something still seems fishy about it.

1) "Yes, I think MWI is true" 58% 2) "No, I don't accept MWI" 18% 3) "Maybe it's true but I'm not yet convinced" 13% 4) "I have no opinion one way or the other" 11%