If you wish for the door opening height to increase you will.
Raising the height of a garage door opening.
Doubled 2 4 s at minimum should be at each edge of the garage door to allow for the mounting of the tracks and jamb brackets.
It is possible to install larger garage doors to give.
Older homes have smaller openings for garage doors making it more difficult to fit modern vehicles in.
Set up your step ladder beneath the garage door opener being certain the ladder is level and stable.
So just get one new panel for each side if you need to raise it up a few.
You d need to put a little jog in the roller track to get the top of the door to do right when it closes but other than that it should be doable.
If you put them higher you d have more clearance with the door open or closed.
The big board with the springs attached is necessary to span the door opening.
It looks like 84 6 your max of 90 or so.
Have you thought about modifying the tracks on the side for the rollers.
Without changing the roof above it appears that the only space available for raising the door is occupied by short 2x4 s or a max of about 6.
These doubled 2 4 s should extend to the ceiling on both sides to allow for the mounting of the end bearings and brackets.
Locate the limit adjustments screws located on the side of the opener.
An exterior shot might help.