The top I removed was the second top the cat wore, so I don't think the glue is too old. I am using a wood chisel to scrape the glue/top backing off, but thought maybe a sander or grinder might be faster and smoother.
Some 40 grit sandpaper makes quick work of it. You need to prime AND paint the roof before installing another top. I recommend a two part primer like PPG brand DP40. Then a topcoat of two part polyurethane.