Gas stove cleaning

I guess it depends on the stove. Certainly, I've never taken off the top. I take off the grills, lift off the black centre spot and lift up the unit that disperses the flame. There are no screws to deal with. Now you should be looking at the basic top of your stove. All the things that you took off go into hot soapy water to be scrubbed (or soaked and scrubbed) if necessary. Then rinse and dry them thoroughly... overnight air dry would be best.
While the "pieces" are soaking, clean the top surface of the stove with whatever is your favourite cleaner. You will notice, after all those "pieces" are off, that the area around each burner is raised from the stove top so nothing could go down the "hole".
It is ONLY if something got down the "hole" that I would even consider having a professional come in to remove the top.
Like all things that need to be cleaned, it's so much easier if you just do a little wipe up daily. I have rented houses with the grottiest looking stove top in creation and never quite understand how it gets that way.
BTW, a stainless steel stove top is DIVINE to keep clean.