Here is a picture of what the sockets look like. I could not find any make or model information on the hardware.

Here is a picture of what the sockets look like. I could not find any make or model information on the hardware.

Thanks for posting. Could you confirm the size of the opening that accepts the track? The correct option will depend on that measurement.
Great, thank you! That makes things a lot easier. I was worried this would exceed 1", in which case we'd only have somewhat involved solution. But we don't have to think about that. Take a look at our 32-119. I think you could possibly use this as a replacement, but review our dimensions and let me know what you think.
You know what, that's a totally relevant point that I should have caught sooner. In that case, I think you should consider our 32-089 instead. The opening is very nearly the same size as the 32-119 (1" x 3/8" vs 31/32" x 7/16", respectively"). The 32-089 does not slope like the 32-119 does, so I think this is the better choice for you. See what you think.