I got the glass through a local shop. My situation was different, as only one wall, the "front" door wall, was glass. The other three walls were kerdi and tile. The sloped glass ceiling was captured in the walls on three sides and clear silicon was used to seal the remaining side to the front wall of glass. I'm not sure what type of specific seal was used on the door. It might have been clear vinyl. If you do a search or ask at the glass shops, it might also help if you refer to it as a "raked" (sloped) front wall of glass. Actually, lemme see if I can get a quick google hit... Found one at Wilson Glass. Not exactly what you're looking for though. Using something like that with a sealed transom overhead would work and be the lest expensive. Having the front wall as a single piece of glass with the door cutout of it would be $$$$$.

You can use a u-channel and there are several really wonderful examples of showers that have been installed with them. TreasureTheDay's stands out as a recent example. But you can also use clips and it will be just fine. We installed a steam shower about two months ago with a set up very similar to yours (fan outside) and used clips with silicone sealing the space between the glass and solid surface. Though it's been hot, we've used the steam shower at least once a week -- it's great for aching muscles after a day of gardening! Your glass installer is quite right that no residential steam shower enclosure is perfectly steam-tight. But even with our transom, we have minimal leakage. It is not a problem. It's tough to get far enough back to get a picture + glare from lights, but here's ours. From Bathroom

We have a semi-frameless, so there are cracks around the door and around the transom window above the door. But when we run the steam there's no noticeable escape. That said, I've never run the steam for more than 10 minutes (it's fairly new) and our bathroom is pretty large (10'x20') so take my experience with a grain of salt.

3M makes a high strength adhesive (in a small tube), maybe even super glue. Just dry both surfaces with a hair dryer before applying the glue.