David Chenoweth, on his blog, does what Amir Omar failed to do: make a legal argument for calling a special election to fill the vacancy in the mayor's seat. It's not a very good argument, but it's something.
Chenoweth argues that even though the charter explicitly says how a vacancy in the mayor's seat shall be filled (Section 3.03), it doesn't explicitly forbid the council from doing something else entirely. This is strange legal logic. It argues that the charter is a document of suggestions, not laws. Let's apply it elsewhere. For example, Section 3.01 says the council shall be composed of "six (6) members and a mayor" but it doesn't explicitly forbid having, say, eight (8) members, so by Chenoweth's logic, the council could name a couple of extra council members and everything would be kick ass. By this logic, the charter review commission better start going over the charter and adding "and shall have it no other way" to practically every section of the charter if we really want the charter to be a document of laws and not merely suggestions.
Chenoweth also makes an un-legal case, namely that he thinks the council is violating the charter in other places, so violating the charter here, too, is just as kick ass. Needless to say, I think that's a really bad argument, too.
Maybe this is why Amir Omar didn't try to make a legal case for a special election. He can't. Not unless he can come up with something better than Chenoweth.