Robert, you have included a lot of things in your post, but I will try to help.
You haven't told us much about your server, but my guess is that you might have a VPS, right?
Before you do anything, make sure that you have backups of your MySQL database, and your moodledata folders. Copy these backups to a local hard disk, just in case you clobber your server doing your updates.
EasyApache4 caught me by a little surprise, initially. Then I worked with it, experimentally, and got the hang of it. Yes, 4 is probably better than 3, meaning an improvement.
In EasyApache4 you get to choose which versions of php you want to include. I did experiment with running both php 5.6 and 7.1, but then decided to keep my new server clean and not include 5.6. I have my old Moodle 1.9 backup running on a local MAMP install. If you do decide to run multiple php versions, you should be able to find a tools that let's you point different "users", or domains, to different versions of php. So in theory, you should be okay, but you will need to know what you are doing. You don't necessarily need a domain name for 1.9, unless you want the world to have easy access to it. It could be just another "user" on your VPS, that you get to as http://[IP Address]/~username.
I upgraded to Barracuda somewhere along the way, and it could have been back before Moodle 2.8. Can't remember. This is done differently, in my.cnf, instead of with EasyApache4.
Here's a suggestion. Might you be able to buy a one-month new server at a reasonable cost, do all of these experimenting to make sure you know what you are doing, before you do your upgrades on your production server?