Thanks to all your great tips, I've finished restoring the speaker

I used brown coffee filter paper and Aleene's Original Tacky glue.
Here's it is all torn up.
First patches applied.
I used some painters tape to hold it together while the patches set up.
Down to just that big hole to fill.
I decide to try making a preformed patch by using a plastic sheet over a good portion of speaker cone.
Then, I cut a suitable piece of coffee filter and soaked it in diluted glue.
It work out fairly well. I was definitely able to capture the curvature, but the ridges aren't very distinct.
Even so, I think it's a promising technique.
Here's the patch in place.
Next, some black acrylic paint. The patch wrinkled a little during the gluing and painting, but I happy with it.
Here's the backside.
Finally, I cleaned up that big wooden plug and screwed it back in.
Is this some type of vibration damper
Here's a
YouTube video I made while restoring the speaker. If you make it to the end you can hear the radio playing