I have something called 'Mosaic Tile Adhesive' made by 'Mosaic Mercantile Inc'. It is specifically for gluing tile to wood, metal, concrete, plaster, plastic, glass and most other surfaces. If it works for ceramic tile, it should work to glue glass to glass. I haven't tried it for the totems yet, but I'm going to use it when making more for this summer. We'll see what happens.
What I've learned is that E6000 works for most things, it's standing water that weakens it. I think it would be OK on the sides of a birdhouse, but wouldn't be OK for the bowl of a birdbath.