You can't duplicate content databases in a single farm.

You would have to remove the content database via the "Manage Content
Databases" link for the first web app, before moving it to another…did you
do this?

At the time, the original content database was still
active when I brought in the restored content database
to the second app. At this point, I've removed the
content database. I've also removed the original
content database, and re-added it, and I'm still
getting the STSADM error indicating that another site
already exists at that URL.

So you removed the content database from the second web app,

And then you removed the original from the first web app, then restored it back
to the first web app right?

Your then trying to do a STSADM restore of the site collection to a "Different
URL", the url in the second web app correct?

If that is correct, and you're still getting the error, I know in V2, there
was a databaserepair operation for STSADM for orphaned entries in the database,
don't know if it's in V3 though, but you might want to check and run that to
ensure that it's cleaned back up.

Restoring the content database into the farm before removing it from the first
web app may have created some orphans when you later removed it

I'm trying to restore the site to its original URL. I
only had the content DB hosted on the second web app
long enough to do a STSADM backup. Once that was
complete, I removed it and tried to do the STSADM
restore to the original web app. That's when the
problems appeared. I tried to drop the content DB on
the original web app and then re-add it to see if that
fixed the problem but it didn't. I'll take a look at
the databaserepair option.

If you are trying to restore to the original URL, with the content database
still there that holds that site, you'll need to use the “overwrite switch
on the restore

I found an orphaned list when I ran the
databaserepair, but it didn't seem to fix it. When I
ran the restore with the -restoremethod overwrite
option, I got this error back:

No content databases are available for this operation.
Create a content databas, and then try the operation
again. To create a content database, click "Content
databases" on the Application Management page, select
the Web application to use, and then click "Add a
content database".

The Number of Sites listing for the content database hasn't reached the Max
Sites setting has it?

No, its not even close. We're using default
9000/15000 settings for this DB

The last thing would check, is to make sure the content database setting is set
to "Ready" not "Offline"

"Offline" simply means no more sites can be added to it.

If it's not that, I'm not exactly sure what might be going on.