I was surprised to find a literature review about probiotics which suggested they may have significant CNS effects. The tl;dr of the review seems to be: 1) You want doses of at least 109 or 1010 CFU, and 2) You want, in particular, the strains B. longum, B. breve, B. infantis, L. helveticus, L. rhamnosus, L. plantarum, and L. casei.
I then sorted the top 15 results on Amazon for "probiotic" by these desiderata, and found that this one seems to be best.
Some points of uncertainty:
I was initially very concerned about this but then noticed that almost all the tested secondary endpoints were positive in the mice studies too. The human studies could plausibly still be meaningless though.
Has anyone (esp you Jim) looked into fecal transplants for this instead, in case our much longer digestive system is a problem?