It's a Staph Infection. You might put a few perches in the cages for them to rest on. A roosting bar will remove their feet from the ground for about a third of the day. Porcelain roosts are available from pet stores. These don't hold moisture and microbes like wooden perches do.
Beyond that, look at where the abrasions are on affected birds. If it's always the bottom of their feet, use a lower gauge wire for the cage bottoms. If it starts above the toes in the leg, it's likely from another type of injury. Make sure the cage wire is folded properly around the edges and there are no sharp wire ends exposed. I always grind down the ends after building a cage. Surprisingly, most commercial cages even ignore that detail.
Make sure the cages are clean. We're talking "Laboratory clean". If excrement is building up and it cannot be washed out in a few seconds every day, that's a flaw with the design of the cages. Sterilize the cages, look for hygienic problem areas (usually the corners), get a wire brush (like used for cleaning a grill) and keep it by the cages for easy cleaning. Copper wire cage bottoms are better, but you have to build them yourself. Staphylococcus bacteria is unable to survive on a copper surface.
Think of the old chinese cages popularized when keeping canaries was fashionable. Cages were round (no corners), of anti-microbial copper construction, using thick wire, and the roosts were centered in the middle of the cage, not on the edges. This made for simple cleaning. In those days, they weren't feeding birds antibiotics or bringing them to the vet. Survival of their pets was predicated on good planning and design work, and they were pretty damn good at it. In fact, the designs of those cages were also very resource efficient, obtaining an optimal interior volume with minimal wire to enclose it.
Even the more squared victorian cages had some very good design consideration, and you can pick up some of them from antique stores pretty cheaply.
Here's a modern chinese reproduction.
These scale up from holding 1 canary to being walk-in aviaries holding hundreds of birds. Yours needn't be as ornate as the one in the picture, it's just there to illustrate the design considerations. A Wire welder and some scrap romex from a construction site will do the trick. You could even work out a no-weld version if you had to.
New cages are not a necessity, they're a labor reducing luxury which could help with this specific problem. Plenty of people have success with cube-shaped hardware cloth cages stapled together. There's nothing wrong with those designs, and they do have advantages in reduced cost and better modularity which are very significant factors. But the Chinese solved this problem a few thousand years ago with nothing but clever design.
The affected birds should be destroyed. It sucks, but remember, 4 out of 20 is a hell of a lot better than their survival rate in the wild.
