Blocking a file is a feature of a particular software, in this case that Sony program.
Blocking a file is a completely valid function which therefore cannot be "fixed".
As a manipulation in MP3tag can result in moving a file to a different folder or renaming it, a player in the midst of playing would suddenly loose the file it is playing. So I think it is ok to block a file while playing.
If MP3tag could simply remove handles from other programs it would become the ideal hacking tool as e.g. antivirus programs could get a virus definition that has been tempered with which in return would open all gates for unwanted programs.
So: no, MP3tag cannot get a higher "priority". But you can ask the other programmers if they really need to block a file for playing. It would be an option to store the whole file in a program administered cache so that the players do not need to re-read the file and therefore would not need to bother if the file is still there.
The blocking actually does not only apply to Mp3tag but to any other program that attempts to write to the file. Such a program could also be an audio editor that cuts away that part that the player currently wants to play. All of sudden the file pointers point to nowhere. An ugly effect.
I just try to shed some light on file blocking. This does not criticize your request but may explain why it is not turned into a feature.