There is a way right now. I’m not sure whether to call it a method or a workaround. I would create the template with a start date of 1/1/2020 or some other round obvious date, and set up all the tasks and dependencies with correct durations (i.e. delta of due date to start date) and the correct offset to the generic start date of 1/1/2020.
When I want to use the template, I’d activate it. There is no way to automatically adjust start and due dates in Asana, but it can be done relatively quickly using the Timeline and the bulk select option in Timeline. Just adjust either your first task or your last task where you want it to be, then select the other tasks in bulk and drag them to the correct timing that correlates to your chosen endpoint. You’ll know things need to be moved either by seeing excess space, or red dependency arrows. It looks like you can move as many tasks as you can grab in 1 screen (no scrolling) of the Timeline; I was able to move 32 tasks simultaneously.