Howdy
Not sure if you have the P250 or the PS250. Mine is the PS250. Same description as yours in re the access door. After taking out the screw, I then reach behind mine via the front wheel well. I pushed REALLY hard on the access panel, and it snapped right out. I noticed four raised tabs [12 o'clock, 3, 6, 9] on the back side of the panel, so I lubed them with Lithium grease.
It has been on and off about 10 times now during periodic checks of the coolant level. Gets easier all the time. Now it's routine for me: out goes the screw, in goes my right hand, PUSH hard, and out she comes.
I doubt you will break it using this method. It is one strong bugger.
Scoot safe and happy
frank