Here's the scenario:
The flight starts night VFR, with broken ceiling at destination (class C airspace) and expected to improve according to the pre-flight abbreviated briefing. I'm IFR certified but prefer to stay VFR to dodge icy clouds along the way.
Now I'm about 15nm from my destination, talking to approach control, and the ATIS calls the ceiling overcast: it's apparent I'll have to file IFR one way or another. Approach is busy, but not overwhelmed.
What is the best way to handle this situation on the radio? I have the ATIS, picked an approach and have a squawk code (advisories):
a). Do I ask approach directly for the IFR clearance, and what is the officially sanctioned phraseology? Also: do I have to cancel IFR when I'm on the ground/see the runway, i.e., is the clearance to descend thru the layer and shoot an approach a 'real' IFR flight plan?
b). Ask approach if I can change frequency to FSS, file with them, then return to approach to pickup the clearance (and cancel when on the ground/view of runway)?
I did read How do you request a "pop up" IFR clearance?. In my scenario I have the time to call FSS, there is no emergency, I'm on flight following and could complete (b) if that's the best way to go.