So did you follow the blogs directions or not?
When you messed with the 'db' directory you were really getting what might have been an older version of MySQL with it's settings as well as the databases (including the DB for the moodle). Would think, but not checked. the newer version of MAMP would have the require versions of PHP and MySQL both in the installer.
At this point, I'm not at all certain of what I tell you to 'fix it'. :\ Not capable of Vulcan Mind Melds!
If you put everything back, does MAMP launch?
How to change PHP versions:
At this page:
It shows a column on the right for PHP versions .... among them: 7.0.x's and 7.1.x's (BTW, think I'd stick to the highest 7.0.x rather than going to 7.1.highest right now. That suggest one can keep the core MAMP in place and just upgrade the PHP.
BTW, the DB for your current moodle is actually in MAMP/db/[nameofdb] ... I have a older MAMP that has a moodle28 and a moodle29 ... those are the names of the DB's that match the separate code directories in MAMP/htdocs/ (a moodle28 and a moodle29). The config files for those two point to their own respective data directories in MAMP/data/ I have a moodle28data and a moodle29data directory which is mapped via the datadir variable in the config.php file of the sites.
IF you going to copy files to move databases, do NOT use the DB directory ... just the folders containing the files for the moodle DB's.
Also check out the MAMP directory from the command line. You should find a .sh script ... mine has a UpdateMoodle28.sh because I started with the 28 version.
That script can be edited using nano and actually upgrade the one Moodle to higher verisons of Moodle by 'side loading git acquired Moodle code' ... add a liine or two and one could backup the code, the data directory, and the DB just prior to upgrading. The script runs moodlecode/admin/cli/upgrade.php so one could upgrade without ever having to use the apache interface.
'spirit of sharing', Ken