It looks convincing to me. It's exactly the same method used to decipher cuneiform, starting with proper names in certain inscriptions and then figuring out the content of other inscriptions somewhat like a crossword puzzle. The fact that one of the tablets turns out to record the syllabary in order is especially compelling.
Funny anecdote from a friend who worked with Linear Elam and was very skeptical of the Desset proposal: When he applied the proposed decipherment to a short inscription on a pot, it read "God condemns who takes this vase", freely translated :-)
Earlier proposals had swathes of special cases to account for inconsistencies. They were not credible. This one works!
It looks convincing to me. It's exactly the same method used to decipher cuneiform, starting with proper names in certain inscriptions and then figuring out the content of other inscriptions somewhat like a crossword puzzle. The fact that one of the tablets turns out to record the syllabary in order is especially compelling.