I have had unbelievable success with a product available from The Rust
Store at https://www.theruststore.com/  It's cataloged as SKU T90012,
Boeshield T-9, 12 oz. Aerosol, $12.99 + $6.95 S&H.  If you have a
marine supplier near you, more than likely you will be able to get it
there and save the shipping cost.

Believe it or not, I had four lamp posts around my house that the
neighborhood dogs loved to mark.  I only found out how acidic dog urine
is when the cast aluminum bases of these posts disintegrated into a
white powder.  That was not the worst part -- I had to try to remove
the 5/8" nuts, washers and lock washers from the 5/8-16 j-bolts that
bolted the poles to their concrete bases.  The nuts had an incrustation
or rust 1/4 inch thick over themselves the bolts they were attached to
and the washers and lock washers beneath them.

When I received the Boeshield T-9 from The Rust Store I immediately
stuck the fine spray extension straw into the nozzle of the spray can
and went outside and sprayed the previously prepared bolt & nut
combination, from which I had removed any loose or easily dislodged
incrustation.  I noticed that this product seemed to be sucked into
the threads of the nuts as if they were being vacuumed in.  Because
this was such a heavy encrustation, and because in my heart I knew it
wouldn't work, I let it sit for 24 hours.

The next day I did another application, just because I didn't trust it
I waited another day.  On the third day -- still apprehensive of
applying a 1/2-inch ratchet socket driver to the nuts and shearing off
the 5/8" j-bolts with the leverage from this tool -- I decided to apply
the spray once more and wait for the following day to destroy the bolts.
On the third day I used a wire brush to remove as much rust as I could
from the bolt area exposed above the nuts.  Well, you can imagine my
surprise when the nuts actually turned.

Still doubting that this had actually happened, as I thought for sure
the bolt itself was twisting itself to destruction, I carefully lifted
the socket wrench a bit so that I could see the bottom of the nut.
Then with the socket half-on and half-off the nut I reversed the
ratchet action, tightening the nut back.  To my amazement, this
impossibly encrusted nut was actually turning on the threads as it
should.  I continued to back off and re-tighten the nut as if I were
tapping a thread and in short order all the nuts were off the bolts.

With new stainless steel nuts, washers and lock washers applied to the
bolt threads and lubricated with WD-40, the posts with reconstructed
aluminum bases now stand on the original bases and j-bolts, waiting for
the next batch of dogs to destroy the aluminum bases.  The last ones
lasted 35 years; I doubt that I will.  Perhaps the next owner of my
house will come across this article in cyberspace and re-do it again.

I think that this is just what you need for removing the tree cup from
the shaft.

Good luck,
Walter Kehoe
Syosset, New York