>However, there is some light evidence that the variation I see is not just intra-day variation. Specifically, there are several species that stay consistent in frequency across all samples: e.g., Neisseria subflava, Streptococcus viridans, Streptococcus oralis.

Disagree. You can not make that claim without sequencing your mouth's microbiome in the absence of probiotics for a month as well (and, really, many more than one persom's). Was your diet controlled all month? Oral hygiene habits? Any of a million other variables?

Also, it's worth pointing out that the study was designed to test one hypothesis, and you need to be very careful about looking at further claims. This test only really provided evidence that these probiotics don't introduce L. reuterii.