And mission accomplished!
Thanks for all the advice. Not sure if I followed it exactly, but I took it into account and I've got a solid floor now with no squeaks... Except one corner of old wood by the door. Where it meets the new, it gives a little and rubs against. Shot some liquid nail in there, so I guess I will see how it turns out once that sets. Nothing else along that seam squeaks, and I didn't think of putting in any support in that area as its right between two joists.
Here's the hole all scraped and cleaned out:
Here's the support blocks I put in because this end wasn't ended on a joist due to the wall, so hopefully this will prevent sagging over time. One end of the block is on a piece of wood above the ceiling below, other end is glued and screwed into the joist.
And here it is finished. I'm happy with how it turned out. It helped a lot by cutting the insert into the right dimension, laying it in the hole, then tracing a line on the old floor where I needed to straighten out the circular saw cut to get it to fit. Went really easy.
Maybe not the biggest or hardest project, but not having used a circular saw before a couple weeks ago, I feel real good about getting it done. Thanks for the help, and maybe a little bit of extra confidence too that I could do it. :-)