Hmmm. If you read the other thread currently active on the board about homemade Best Press, the info presented there states that the starch from the vodka does not stay in the liquid, it turns into alcohol. The yeast eats the starch and the by-product is alcohol. Also, if you're using the recipe posted in that thread, it's incorrect. It's missing starch. You can use a product like Sta-Flo, or cornstarch. There are several recipes on the web, here's a couple published by a couple of nationally known quilters.
http://dianegaudynski.blogspot.com/2010/02/starch.html - a corn starch recipe.
http://www.marklipinski.com/Tulip%20Tips/TTcontent.html - a liquid starch recipe. Scroll down to tip #1. He also has a "lavender linen water" recipe as tip #3, it is the same as the recipe the OP tried to use as starch.
I believe that the vodka acts as a preservative to stabilize the starch so it doesn't go bad.
I'm with the earlier poster - I've got better things to do with my time, the cost of starch is relatively low in comparison to the hassle of actually making and storing a homemade version.