How do you get a stuck inner drum out of a Kenmore top loader?

No hidden clip or set screw on the 110 series. The basket just sits on the drive hub, and over that many years the aluminum and steel corrode into each other and it becomes one solid piece of metal. So yes, it's purely a corrosion fight, and you're doing everything right so far. The people who get these apart are the ones who keep at it longer than feels reasonable.

The thing that finally worked on mine was a lot more force than a rubber mallet can deliver. I pulled the whole outer tub and set the assembly on the floor, then used a hydraulic bottle jack under the basket with a short length of 2x4 on the jack pad pressing against the underside of the basket rim while the shaft hung down through the floor opening. Once you can put a few thousand pounds of steady pressure on it instead of taps, it goes with a bang rather than a millimeter at a time. The bang is startling but that's the good sign, that's the corrosion bond letting go.

If you can't get the tub assembly out to work on it flat, a bottle jack up through the agitator shaft opening with wood blocking on top can still work, just harder to keep everything lined up.

On heat, be careful with a torch on that hub area. There's a seal right there and the plastic outer tub isn't far away, so it's easy to make a much bigger repair out of it. If you want to try heat, a heat gun kept moving on the hub only, plus more penetrant while it's warm, is about as far as I'd go.

Realistically, budget some time. Soak it, jack it, let it sit under load overnight, re-soak. The bond ussually gives up on day two or three, not day one.

Been down this road on an older top loader and yeah, patience is the whole game. One thing that helped me besides soaking was hitting the hub from the side with a hammer at a slight angle while someone else pulled up on the basket. Side blows seem to break the bond better than straight-up taps. I also re-soaked every few hours instead of once, wich I think mattered more than the oil brand. Don't rush it and crank on the basket itself, those old plastic rims crack easy and then you're buying a new basket too.

Following this because I'm probaly headed the same direction soon. Mine's a diffrent brand but the symptoms sound identical, basket that hasn't moved in years and me with no real tools to speak of. One thing I noticed when I had mine apart partway: once I got some movement, the hub started turning with the basket instead of the basket lifting off. Is that normal on these, or a sign something's seized further down? I don't want to trade a stuck basket for a stripped shaft. Also curious if a proper gear puller gripping under the rim is ever an option, or if the rim just bends first.

That spinning-togehter thing the last guy asked about is normal, mine did the same. The hub and basket turn as one piece untill the bond breaks, it doesn't mean anything sheared. What got mine loose was a long pry bar under the basket rim braced against the cabinet opening, working it up a little on one side, then the other, back and forth while it stayed soaked in penetrant between sessions. Two evenings of that and it popped free with zero warning, nearly took my face off, so keep yours out of the drop zone when it finally lets go.

That jack setup is the way, same thing finally got mine off a 90 series. One detail that helped: I put an old drive belt around the basket rim so the wood block had something to grip and wouldn't skid off when pressure built up. Mine sat under steady load overnight and let go around midmorning with a crack I heard from the other room. Also put a tarp down first, because when it breaks free the rust water underneath goes everywhere.