I had a similar problem. For me it took a while to get a feel for how much back pressure and when to apply it so that you stop with the cranks roughly horizontal. Having such a high gear ratio probably doesn't help, but it's probably doable. You also have to get over your ingrained fear of falling once the bike comes to a stop.
I learned to trackstand without riding into it. Straddle the bike and put the cranks at 12 and 6, put your back foot on the lower pedal. Push the bike forward just enough to make the cranks horizontal and step up onto the other pedal. Flail until you stay balanced. It helps at first to have something like a stairstep that you can run into with your tire and prop yourself up for a couple seconds.