Pick swirls

I’m planning to give a little TLC to my No. 1 Axis, do some things that are overdue and some things that it just deserves after 10 years of service. One of the things on the list is to try to buff out the pick swirls in the finish below the strings. Apparently I beat that spot up when I play. I’ve used polish on it, but that really doesn’t do anything to remove the scratches, so I’m wondering if anyone has any techniques they can share that are safe and will shine it back up again.

It’s not that big a deal as they’re hard to notice except in the right light, but if I’m doing the job, I figure I should do it right. 🙂