At the moment I seem to be able to set the device period and buffer just with the BASS config with both the latest and beta versions, with and without the DSOUND flag, but it's definitely nice to know about since that is a much easier solution than having to go through the BASSWasapi addon in order to specify those, and I'm going to continue trying to figure out if I can replicate that behavior from before.
To try and clarify the actual problem I think is being encountered, it's some sort of a desync/delay in how long it takes for the sound to actually play. I seem to be able to reproduce this desync with larger values for the device buffer or update period, so I suspect that the delay is being caused by the time it takes to update the device buffer. My reasoning for thinking this is related to WASAPI is because in the BASS documentation for these config settings, and as I previously saw myself, it says that these settings usually won't have an effect on Windows systems, and that Windows will decide the actual value. The theory is that Windows is setting these values a bit too high for our case in some cases, and causing a slight desync. If this is the case, then originally I believed that the solution would be to use the BASSWasapi addon in order to tell WASAPI that we want lower values, although specifying to go through DirectSound might be the better solution.