Let's start with this:
"Another trial could be have the full list of tables involved in such
students interactions and only get and import such information from the
backup. Is the list you provided, the full list of students
what I provided was a very poor example but thought it might suffice to describe ... no ... list provided not full ... there are probably near 3-4000+ tables and remember, MySQL/MariaDB is a 'relational' SQL DBM.
Would take the skills of a MySQL/MariaDB guru of guru's me thinks. So entire DB would be best.
Bad news 2 ...
"error saying my installed version of moodle is different than the imported database and can't continue."
You have 3.6.x code and DB is 2.9.x. The import of last SQL was for 2.9.x code.
fix ... restore your backup taken just prior to importing ... the code you did not touch ... right? moodledata/filedir you did not touch ... right?
If so, restore of DB only thing needed to get back to square one.
Now moving forward ... if the last sql dump they gave you was for site and version 2.9.x and moodledata but no code, get the 2.9.highest code using new DB dump and moodledata should result in a minor update ... 2.9.x to 2.9.highest.
Then begin the march to 3.5.highest again. If you were using git repo for code, could probably get'er done in 4 hours or a day ... depending upon size of site.
If not using git ... painful, yes ... probably cursing all the way, but .... :|
Know you might not want to hear this now (virtual finger wag) ... but next time ... get a cutoff date/time in writing. The site in maintenance mode on that date/time and doesn't come out until transition/upgrade is finished - no 'backies' ... no 'oops'! ... no 'I forgot this little thing ...' ( ... little things are many times not so little!) :|
And the other take away ... thank goodness this one you knew ... backup ... backup ... backup. Through the march be sure to do a backup of DB and code (moodledata changes very little if at all ... only caches) so one doesn't loose ground if hickup happens ... and we all know, hickups can happen! But you've had practice (groan) so no hickups ... right