Run the Migration Assistant utility on the new computer, and it'll walk you through migrating the account to the new computer. It's actually good that you used a different name on the new computer, since that means it can bring over the entire account (by its original name) and it won't conflict with the account you've already created on the new (/temporary) computer.
Fastest way and best way may not be the same in your case, based on the info you provide.
Since you have found that Migration of apps bring the slow performance back, I'm not sure I'd do any more migration, but would try re-installing the apps instead. This would create new preferences, eliminating an "bad, old preferences" that may have been the cause of the slow down.
Re-installing will take more time, and apps like those from Adobe that require key #s are going to be a pain, but the end result of a properly performing Mac is your goal.
The problem with Migration is that it can bring the problems with it, as you have seen.
The problem with re-installing is that you will never know which caused the problem. You won't be able to avoid creating the problem again. It may not have been anything you did, but a built-in glitch that is going to occur whenever a particular set of apps and actions are present.
Perhaps a faster way to solve the problem of what causes the slow down:
Make sure all 3rd party apps are in the Applications folder, or have aliases there, so all User accounts have access to them. Then log out of your account and into another account and test for performance problems. I have an account called "Test" (non-Admin) just for this purpose. This account will have its own preferences for those apps, different than yours.
Now, in that Test account, start using the apps and your Mac, watching for slow-downs.
Whatever you do to solve this, please come back and report it- what worked and what didn't. We all can learn something from it.
Best Answer
The best way to migrate is to make sure you have a current Time Machine backup and just restore from that volume to the new machine. I have restored from a Time Machine backup to an empty formatted hard drive and it worked perfectly, including my custom FTP, HTTP, and git configurations. It took about 10 hours for a 1TB backup.