If these are from the 70's and 80's you might not be able to find pads that fit properly anymore. Though I've made some work with my old bikes. But yes cleaning and maybe sanding the pad a little might help.

Your 500's are similar to the Weinnman 605's that were on my Raleigh, or at least close. While I grew up on such brakes when they were new years ago, they never were great at stopping the bike to make you feel comfortable. Although they always stopped me in time for any stupidity on my part or others when I needed to stop quick.

So if you ever get around to the point you want to spend a little more on the bike, look for some double-pivot caliper brakes to put on that bike. They'll generally give you much better stopping power than the single pivot brakes of vintage days. And they really aren't very much cost.

As you've already found out with the Shimano 600 brakes, caliper brakes come in different reaches. Simple to say that they are either long reach or short reach. And you have to look for the correct mounting type. Some come new with the stuff to let them mount several ways. Some only mount one way.