I'd start the 10th with a runner on 1st. Then start any subsequent innings with a runner on 2nd. With the three batter minimums it just seems like too much change.
Although, it did make last night much more exciting.
I hated the runner on second at first but I'm starting to really like it. Like you, nfotiu, I'm surprised at how much strategy it adds (at least at first). Big advantage to being home team, also.