Impact driver always works for mr but if you aren't careful and booger up the screw head you will not get them out easily.
If you have to remove the heads, using a dremel with a carbide ball bit is the best way to get a hole started without marring up the cover and having a drill bit wandering all over on you.
You have to be careful of the carbide bits because they break off easily and aren't cheap.
I even keep a set of left handed twist cobalt drills for frozen fasteners. Often the heat of drilling helps free up the threads and the left hand drill rotation backs them out as you drill.
There is a product called AERO KROIL made by KANO LABRATORIES that does work better than PB Blaster. I have a gallon of it but they sell spray cans. It's expensive and you used to only be able to buy it mail order. But I think I've seen it on Amazon recently.
They print right on the container; "The oil that creeps" and it does. I've proven it many times when using the stuff. It's amazing how it works it's way into impossibly tight, rusted up places.
But...IF you're in a rush....it's not fast at all. I have waited up to a month or more for it to work on frozen sleeves on shafts. It's just the way it is. Heat speeds up the penetration of KROIL and PB Blaster but it's not really an option around those plastic covers.
When you get the screws out, replace them with socket head screws because they will be hard to get off next time too. I think HONDA now ships the newer engines equipped with socket heads because those little Phillips screws are such a pain.
Now...if they would only use something more user friendly on the gear case drain and fill screws that would be a big improvement too.
Good luck.