Pardon again ... but .. me thinks you are looking for an easy button that doesn't exist!
"I can't migrate a server from Digital ocean to AWS."
Yes, that's probably true ... not the entire server for obvious reasons. The only way to *move* a moodle server from one provider to another is backup and restore.
Now this is key ... "We're forced to do this due to infrastructure issues."
Because you haven't answered, assuming that to mean your moodle at 2.9 doesn't have the resources it needs to run ... space, memory, etc. So your account with them is a 'shared system'.
Your path of least resistance and complication and expertise to admin a system (just being honest) is to move from Shared Hosting to Dedicated VPS with Digital Ocean.
After you get more resources and on a VPS system, upgrade the 2.9.x to 3.6.x in stages. Then, if you still want to go to Amazon, it should be easier to backup the moodle code, the moodle db, and the moodledata directory on DO system, transfer those backups to your Amazon system(s) and restore there!
'several hundred users' ... means how many ... exactly? iMHO, that's not a large site. While Amazon is powerful, do you really need it? You could be attempting to setup a "caddie" and never drive it past a 4 door chevy ... so to speak.
My 2 cents of course! :|
'spirit of sharing', Ken