From your description and from looking at pictures, the Schaller seems closer to my way than yours, as the rollers appear to be smaller than the string diameter, not larger, creating two contact points on either side of the string. I'd wager that Schaller's design was that smaller was better than larger in order to keep the string from wobbling in the saddle.
Yeah, in all fairness the Schaller is a sort of a soft V shape. The problem with the Schaller is the strings pop out of the saddles too easily. You have to make sure the saddles are high enough to get good downward pressure. Schaller supplies spacers to rase the bridge up, which seems like a good idea for a high neck angle, but then the saddles are low to the bridge plate and the strings rattle and pop out of the rollers.
I've had to cut deeper wider slots in the Schaller rollers on more than one occasion to keep the strings in place.
All this is hardly more than academic anyway. I certainly agree with you that Badass bridges aren't worth the trouble at all, if for no other reason than the endless debate they constantly seem to spark among bass players. I only have one because I bought it years ago.
It's a good bridge if it fits your string spacing well, and you don't plan on radical string gauge changes. I think the Schaller bridges sound similar and are more adjustable, as long as it works well with the bass' neck angle. I've used some Gotoh bridges I liked, but the bridge was too high, and had too many damn parts. I had to remove some of the saddle parts and cut slots. I'm trying to avoid that.
I'm not a big believer that there's any audible difference from one bridge to another, as long as they are mechanically sound and properly set up.
Different materials certainly do sound different. I'm not nuts about brass bridges. I don't like the top end. Steel is snappier, which is probably why Hipshot used steel saddles on their new bridge. Aluminum almost sounds like a wooden bridge, but with more mids and highs.
Now for each material the bridge design makes a marginal change in tone. The biggest thing is mass. More is not better of worse than less, just different. Compare a stock Fender bridge to a Badass for instance. You will hear a big change in tone. But it still sounds like the same bass.
I used to put Badass II's on my Ricks. They still sounded like Ricks, but with more sustain and a smoother tone.
I actually don't like any of the bridges on the market 100%. I'm currently working on my own design.