OP:
I don't know how far you've progressed as I write this, but I'll offer my thoughts.
I've done "manual migrations" as you're suggesting above, but be aware that doing one is more complicated than using Setup Assistant (which runs at the close of the initial setup process) or Migration Assistant (which can run any time).
First and foremost, if you create entirely NEW accounts on the NEW Mac and then try copying over stuff from the old one, you're probably going to run head first into permissions problems. This can be easily worked around, but you have to be aware of what to do.
I've never used Time Machine, so I have no idea how one would copy folders/files from a TM backup to a new account.
Instead, I have always used cloned backups created with CarbonCopyCloner. These can be mounted in the finder and browsed through like any external finder-mountable drive.
You should do this first:
1. Mount the backup drive, let it appear on the desktop
2. Click ONE time on the icon to select it, then type command-i (eye) to bring up the get info box
3. Go to sharing and permissions and click the lock icon and enter your password (the one for the administrative account on your new Mac)
4. Put a checkmark into "ignore ownership on this volume" and close get info
Now you can copy ANYTHING from the backup drive into the new account, and the copied items will assume ownership of the new account.
VERY IMPORTANT that you are also aware of this:
You CANNOT copy the top level of sub-folders from one old account to another.
By that, I mean you can't copy the folders named "Documents", "Music", "Pictures", "Movies", etc. I believe these are symbolic links and won't copy.
HOWEVER -- you CAN copy items that are INSIDE these folders.
By that, I mean that you can open your Pictures folder, select items inside, and copy THEM into, say, the Pictures folder of your new account.
Also be aware that you can copy some stuff (perhaps not all) from the home/Library folder into the new Library folder as well.
There are many "nested folders" inside, so it's probably best to have a clipboard and paper on it to keep a record of "what's copied" as you move along.
For a good manual migration, better set aside 3-4 hours or maybe more. It's going to take a while.