I didn't feel like my adjustments resulted in quite the right setup so I put the bike on a stand and dug in to see what was going on.
What I found was that there's a minor problem with how Evelo is building these bikes that makes adjusting the drop out for belt tension problematic. Luckily, it's pretty easily fixed.
First, here's a close-up of the left side drop-out, with the axle in place:
In that photo, the axle is all the way into the drop out, which is good, and ready for the axle locking piece and 15mm nut.
Here's the same view with the wheel removed:
The shiny black is the frame, the matte black is the adjustable drop-out piece. If you loosen the two screws, the adjustable piece should slide to the front or back. What I found was that these pieces don't slide well. What's going is a combination of the screws deforming the frame a bit, and also the paint creating an interference fit.
I ended up removing the drop out pieces completely and gently filing the oval opening so that the drop out piece can more easily slide:
Then I reinstalled the drop-out pieces, installed the wheel axle nuts, and then was able to adjust the belt tension and wheel centering within the frame.
My recommendation is that if you need to adjust the belt tension or wheel centering, that you
first remove the wheel completely, then loosen the drop out 5mm hex bolts (blue arrows in earlier posts). Then see if the drop out piece will slide to the rear with hand pressure. If it won't then remove it completely and clean up the paint inside the oval until the pieces fit well and slide pretty easily. Then reassemble and adjust. BTW, the frame hanger appears to be steel while the movable drop-out piece seems to be aluminum.
What happened to me on the other side was that the drop-out piece didn't re-seat flush against the frame. I didn't do any real damage to the bike, but things just weren't lining up right. It's aligned much better now.
I had to adjust because my belt tension wasn't high enough and at very low speeds standing on the pedals to get going would make the belt skip a tooth at the rear. It's maybe too early to tell for sure, but it hasn't happened again since I tightened up the belt. I may invest in a real tension gauge.