Let some air out of the tire and start kicking it hard to move it back and forth spray the gear box and cable and try again
Kroil Original Penetrating Oil (Drip-8oz Can-Single) | Penetrant for Rusted Bolts, Metal, Hinges, Chains, Moving Parts | Rust, Corrosion Inhibitor (KL081)
https://a.co/d/iErR4PU
Sea Foam Seafoam Extreme Marine & Rv DC-14 Seafoam Deepcreep Aerosol 12 Oz.
https://a.co/d/iBWKHnW
There are a few junk yards in Nevada find a “pick a part” and or call and see if any of them have the spare carrier gear.
I just check ebay inventory and they have an assortment of new and used for under $90