if you have an impact driver, put it on the socket and spray the socket with a bunch of wd or pb blaster (my preferred), without pushing on it run the socket F then R a few times. get it turning then gently pull while running the impact to turn the socket.

like bob said, it helps if you can freeze the socket too, not sure how to do that effectively though.

if you have a welder and don't mind sacrificing a socket and extension, weld the extension to the socket with 3-4 hard tacks.

I've been spraying with PB blaster and tried running it back and forth. It's far more stuck than a regular extension will allow for (extension just pulls right out even after PB blaster and running it back and forth). I'm going to try to pick up one of those locking extensions to see if that will help.

I've been thinking about freezing it, but it's so far down in there I'm not sure how I could do it.

This may be the direction we end up going....I'm just not sure we can get the welder that far down in there

What the heck was toyota thinking making those plug tubes irreplaceable....

Have you tried peeing on it?

Possibly a blind bearing puller?

update?

I guess my first thought was.
Why are you changing the plugs?

That’s all I have.

Gall or scruff up the end of the extension to a point where you need to tap the extension into the socket with a little force (LFH) so it would grab more. Use a different socket to gage just how much you need to deface the extension while still being able to get it in.

Maybe pour some lighter fluid in the hole and light it so it burns out the rubber socket insert while you try to pull it out. I would do several attempts at this.

Here is what I would try after exhausting all other ideas.

Get a long socket extension (like 12 inches) and align it in the socket and mark it so you know where it will slide in the socket (for the 2nd part if needed). Ground a welder as close to the socket as you can and then put the extension into the stinger. Push the extension in the socket and get ready to start pulling the socket out and have someone turn on the welder while you slowly pull up. Turn off the welder as soon as you feel it pulling out so you don't arc out on the walls. If that doesn't work, carefully slide the extension down into the tube (not touching the sides of the tubes) until you arc the extension to the socket for a few seconds then try to shove the extension into the socket (with a BFH if needed) while it is still hot and immediately shut off the welder.

A couple of recommendations for you - don't be sweaty while you do this in case you ground out and blow a fan across the engine bay to minimize any flammable fumes and have a fire watch standing there with a couple of extinguishers handy.

If it works you owe me lunch but if it don't and you either kill yourself or burn up your car than don't try to contact me as this is not to be construed as professional advice.

Can you spin it with an impact and apply upward pressure with channel locks ?

If all this fails, watch every Youtube video you can find. May be some new ideas there.

You say you can turn the socket if you put a lot of force on it.
Have you tried turning it down/clockwise to see if you can get the socket unstuck?

I'm guessing that was the first thing you did but its all could offer.

Vise grip and a slide hammer or pry bar.

All my guys voted. They said this.

Get a long screwdriver that is 1/2” wide at the tip. Flat blade. Take a grinder to the tip of the screw driver and make a big flat hook on one end. Stick the tip into the socket and turn it so that the hook engages the 3/8” square opening on the socket. Turn it while gently tapping the screwdriver upwards with a hammer. Spray a lot of liquid wrench down there while it’s going.