I doubt your sony head unit puts out 20wrms. Theres no guarentee that the OEM puts that out either. My 2006 model Pioneer puts out 22wrms, and thats high. Many of the newer year units are putting out 18wrms. (though sony does have some good power in their radios) Plus I think radio amplifiers are measured at 10%THD.
The cars manurfactur is Harmon Motive. Which if I recall is a sister company of JBL.
You can put more than the RMS value into the speaker, and it will hold fine. Not monsterous ammounts, but Its better to overpower a speaker verses underpowering an amplifier. If you want the most power out of your OEM setup, get a low pass filter rockin on the doors.
And you can always hook up a test speaker to the rear subwoofer to verify that it is even reciving signal in the first place (so you don't get a new subwoofer, and find out that it's still something else.

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Also to add, I'm driving the oem speakers with a 35/70wrms amplifier.