I have quoted bellow here some posts I wrote detailing both (i) my further research sources beyond the ones you mentioned; and (ii) my thinking process in determining what to look out for when trying to analyse a firm's practice areas beyond Chambers/Legal 500 rankings. I think you may find them quite useful. In conjunction, I feel they encapsulate the basic research "theory" I relied on when working as a Law Firm Profile Writer for TCLA, and which enabled me to write profiles like the
Davis Polk one. However, please do let me know if you have any other questions about researching firms in general, or researching DPW in particular.