It took me some Googling to nail down the question “Where does MAMP’s phpMyAdmin (PMA) store mysql databases in OSX?” so I thought I’d summarize my findings.  The reason mysqldump isn’t as convenient is that MAMP is purposely GUI-focused, so switching brains and trying to navigate Terminal to MAMP’s mysql core is annoying and not intuitive (MAMP stores things all over the place).  Also mysqldump doesn’t easily like dumping all databases.  If we’re GUI, then let’s see if there’s a GUI solution and voila there is.

• MAMP’s PMA stores its database files (.frm) inside HD/Library/Application Support/appsolute/MAMP PRO/db/mysql
• Simply navigate to that folder and zip up the entire mysql folder (be wary there is also a separately named mysql folder inside this folder, ugh).
• Throw that onto your Desktop or backup drive.
• Let’s say you return to a fresh install of MAMP PRO, navigate back to that folder and copy all the files including ibdata1, ib_logfile1, ib_logfile0 which contains all the permissions and sql structure for phpMyAdmin.
• Restart MAMP (which restarts mysql) and PMA should be refreshed with all your databases like nothing ever happened.

Similarly now you know how to cherry pick from old Time Machine backups instead of needing to setup the MAMP environment all over again.   Of course different versions of PMA may have changed that db folder structure, so be wary of that.