Hi Daruis!
It sounds the same as my 940...my 780 doesn't have dash speakers. I think Infinity sold a 3" speaker as part of a component system. I was going to try them but decided like you to just live with them. I think you might want to consider the bass blockers. They are cheap. I have some around here somewhere but I'm not sure where right now.

As for the door speakers, are you talking about the front or rear doors? My 940 had front door speakers but not rear door. It was like you said - the grille was there but the door panel fabric was solid behind it. I just cut through the fabric with a utility knife and there were the wires! They were even hooked to the radio as rear speakers. I just plugged in the new speakers and mounted them. If you don't have speakers in either front or rear doors, I would wonder if they are there. Hopefully, yours are the same as mine. Make a small careful cut first and feel through with your finger to see if there are wires.

Let me know what you find. You are welcome to what little I know from experience.

Blessings!
Patrick