Hi Svein,
I don't have a Tyros, so my registrations won't work for you.
I have also found the accompaniment too loud for the right hand playing.
So, I always turn down the accompaniment to a volume of about 80, then turn up the main volume.
Now the right hand voices will be much louder...!
I save this setting in all of my registrations.
Also, if you decide this volume adjustment method works for you, I would suggest that you then buy a volume foot pedal, so you can still turn down the right hand volumes if necessary.
Another way to get more right hand volume would be to decrease the setting of the velocity sensitive keys.
If you turn it totally off you will hear some very loud pianos & guitars for sure!!
I believe this setting would not be controlled by the registrations, it is in the 'global' set-up of the whole keyboard.
Hope some of this helps...