This is a very interesting post. 

I'd lean toward the latter, but I just don't think we know. 

Or you'd be persuaded if they switched "a" to "i" back to "a" in biologically implausible time?

This is handwaving. To make such a claim, you need reference to the mechanism or at least the anatomy. As a source, sperm whales don't have a larynx, but they have phonic lips. As a filter, they don't have tongues or lips or throats in the way we do, but they have a distal air sac. Is that what they're "changing the length" of ? Is that what they're "changing the tension" of? 

"I think for your speed argument to be relevant, you need to show that the whales are switching between sounds at a biologically implausible speed". Yes, this is exactly right. Look at Fig 6 above.

The spectral pattern switches from "a" clicks to "i" clicks in at most 100 ms (there might be 30 ms between clicks and each of those click samples is 5 ms). That's really fast. It rivals the human motor system governing our articulation. It's ambitious to claim whales have such capabilities without detailed anatomical references that the authors don't make. 

As I noted elsewhere in these comments, the intracoda timescale is borderline as well, and would rival human abilities. A huge claim.

I hadn't considered the overtone issue. I need to think about that... 

The intraclick and intracoda "adjustment by muscles" is precisely what I'm disputing. 

There are several possibilities that I hope sharpen this up.

1. The whales have motor articulatory control at the intraclick level, which is why you see the different spectral "vowels" in a single click. Since you see this in 5 ms intraclick samples, they must have control on those timescales or smaller. As the bird people I cite above state, this seems completely implausible, possibly by several orders of magnitude in time. For what's it's worth, my correspondence with the authors on pubpeer makes it clear they're not claiming this.
2. The whales have motor articulatory control at the intracoda level, which is why you see the mixed coda types (Fig 6.). However, the spectral change you see in these example occurs within at most the 100 ms range (like you said, say maybe 10 ms per click plus 30 ms in between) which is about human-level abilities. Unlike 1, this isn't completely implausible, but it seems like a very ambitious claim.
3. The whales don't have motor articulatory control at the intracoda level, and the mixed codas actually represent a beaming artifact/interference pattern of the kind outlined in the post. However, once you concede that, it becomes parsimonious to say that actually "i" vowels are themselves a beaming artifact. This also explain the intraclick pattern as well. 

It's a little unclear, but I think the authors are claiming 2 is correct. I think they'd need to concede intracoda articulatory control to get this to work (or at least to explain the large minority of mixed-type codas). I'm claiming 3 is correct. 

The mixed codas seem like strong evidence against this view, or at least strong evidence against the claim that the "a"/"i" are an example of what you're describing. 

This is a great point with regards to how plausible the various scientific animals communications claims actually are, but to my eye, the CETI people look motivated in the same way as the Koko people or your local crazy cat lady.