Probably, you can't.
A quick look at the documentation:
ThreadPriority Enumeration (System.Threading)[
^]
says:
The operating system can also adjust the thread priority dynamically as the user interface's focus is moved between the foreground and the background.
So if you set the process priority to "Normal" (the default) windows can "downgrade" it to "Below Normal" when it doesn't have the input focus to maintain the user experience.
It may be that you can set it to "Above Normal" to get some improvement, but you risk "locking out" the UI for your existing app.