You are exactly right.
This was originally set up to be voted on in the General Election in November. The Dem Governor (soon to be ex) sued to move it to the Primary Election. It ended up going to the Missouri Supreme Court (Liberal) and they put it at the Primary Election.
The Gays thought that Primary turnout would be light and they could get their groups out in force. The didn't realize how energized the electorate would be.
Can you say BACKLASH??
Nope, it was not the gay and lesbian organizations that wanted this vote sooner rather than later, it was Rats, both for and against the amendment, who did NOT want massive voting on the part of fundamental Christians, because they also tend to pull the lever for Republicans when they get to the ballot box. Clearly, with the polling data off by a wide margin, there must have been some people who didn't make it into the "likely voter" category (because they didn't vote in the last election), who came out to vote for the amendment.
I thought this was an issue that the Republican Party had a big chance of overplaying, but it seems that they have not done so, they've used it quite masterfully. It is also fortunate that most all of the marriage amendments will be in "red" states, and will not drive out a liberal turnout.
Oregon, excepted, of course