Is it worth of replacing central AC coil?
Ok if you know 100% it is the coil that is an easy repair. The refrigerant first needs to be recovered the old coil cut out and the new one installed. Coil cost 2 ton R22 ~300$  Plus recovery time and pumping the system down once the new coil is installed. Measure the amount of R22 returned to the system and add the difference for your ~4 lb total . The repair cost would be 1 days work the coil and a couple lbs of r22.
Dang the 8k and 10k prices sound crazy to me it is only a 1 day job ok possibly a day and a half if access to the air handler is not so good.  But I know R22 is going for 100 per pound 2 lbs plus a coil 500$ in materials ok a a little for the silver solder and flux but other than that the tech time maybe 100 /hr or so it depends,  you might get a guy that needs the extra day of work and gives you a onetime good deal. But those are ball park numbers you could work with so you have an idea.