Hi @kbenmd,
I think QIIME 2 might have what you want.
For beta diversity:
Have you checked out q2-longitudinal? longitudinal - Microbiome marker gene analysis with QIIME 2. I think thepairwise-distances might be what you are looking for but there is a ton of cool longitudinal analyses that might be useful!
For differential abundance:
ANCOM-BC2 is able to account for repeated measure so that would be my recommendation for differential abundance. ANCOM-BC2 is also available in QIIME 2. composition - Microbiome marker gene analysis with QIIME 2
Here are the docs I like to reference when using ANCOMBC2 for repeated measures: ANCOM-BC2 Tutorial
I hope all this helps