[Old Mechanic]

Have the battery refurbed, keep the oil full and replace the cat. Drive a couple more years and look for a replacement.
How much oil consumption? If not more that a quart in 1000 miles then the cat will last, below 500 per quart and it will eventually get contaminated. I had a customer move to Cali and his Z was using quart in 500. He drove it across the country against my advice and it passed Cali emissions for a 1976.

 

[Old Mechanic]

The two worst spots I see on the cylinder walls look like it sat without the engine moving for a fairly long time, top ring with valve slightly open to allow moisture in cylinder.