Nice idea with the templates. I've often thought about a magnetic solution for additional precision, but it would take waaay to much work to implement, and might not work as intended anyways. My thought was that you could install a pair of magnets at the edge of each template, flush with the edge. Then repeat on the bases themselves.
Then, while moving, you firmly place you hand on your base, bring the template to the front, it will fully seat. At this point, you firmly place your hand on the template, remove the base, and move it to the front, where it will firmly place onto the template. This would lead to a lack of "wiggle" room in the template/base interaction.
And if you do it right, you could end up attaching the 3 straight and 2 straight onto the ends of the 1 turn (or anything else) to extend for those pesky bumps. For example, if the top right was always facing North on the template, and the top left was always facing South (and therefore the bottom left = N, bottom right = S) you should be able to have them attract to each other as well as the correct side of the base.