Very slow file copy to encrypted disk image

I would guess that the weakest link isn't the choice of formats, but your picking a decent password and not letting it get observed or captured.

In the general case where there is a system tool and a third party one, I usually start with the tool that is built in until I have good, definite and enumerable reasons to not use the default tool.

Go with encrypted disk images in the case you have set out.

Not sure what the "please fix the library" message means but all of your data is encrypted on the boot partition. You can use a disk password, recovery key or allowed user passwords to unlock a FileVault disk.

When you do it the "normal way" as you mentioned above you won't end up with a disk password. No big deal.

It sounds like User 1 isn't allowed to unlock the disk in this case. You can use the fdesetup command for things like this. For example, to see which users are allowed to unlock the disk:

$ sudo fdesetup list
Password:
macmanager, 51361A22-B6F2-4384-8E0D-F4973BE74957

While logged in as any user you can look in System Preferences > Security & Privacy > FileVault and if some users aren't allowed to unlock the disk there will be a warning with a button to enable users.

You can also use fdesetup to add users to the list, assuming you know their password:

$ sudo fdesetup add -usertoadd davem
Enter a password for '/', or the recovery key:
Enter the password for the added user 'davem':