Copying all my data to new disk, without resorting to Time Machine/Migration Assistant or cloning
The answer is simply no, because no program will be able to know all the specifics of installed programs (MA probably comes closest to 'knowing' most of the specifics of Apple software but as you found, it did so for 99% only), much less drivers, **nix level installes (MacPorts, etc.). 

If you have a well working copy, then clone the disk (SuperDuper, etc.) and then upgrade the new disk to the new operating system.

If you have trouble with your current installation, make a fresh install, then plug the old disk into an USB case and coppy the /Users/(you)/ folders.  This will avoid installed software , old drivers etc.  Then install the software you need (most of it will pick up the essential config data from /Users/you/Application Support/). 

The first is quick and painless.  The 2nd usually is still quicker than you mostly think and gives you the nice good feeling of a fresh start :-)