HV, I think you had a blonde moment or maybe a senior moment there! Pick whichever one applies!
If you had googled <KME capacitor>, you would have found that KME is the model family. The shield logo tells me that the brand is United Chemi-con aka Nippon Chemi-con which is one of the top brands. The first Google hit is the link to the datasheet:
https://www.westfloridacomponents.com/mm5/graphics/datasheets/3/KME-Series-Nippon-Chemi-Con.pdfI'm suprised to see them fail under the relatively benign operating conditions of a linear power supply. They tend to be almost bulletproof. But I guess that after 20 years, anything is possible. I wonder how hot those heatsinks get in normal operation.
You said they're bad, but you didn't mention how you determined that.
As for replacing them, check the AC voltage coming off the red leads. How does the peak voltage compare to the 35V rating on your capacitors? I suspect that there might not be a lot of safety margin there.
I'm also suspicious of that schematic. When I look at the lower bridge rectifier and the circuitry around it, I don't see any big filter capacitors on the input of the LM337 and the lm2940. But they claim to have polarized capacitors of 0.01uf and 0.015 uf. Be cautious about trusting that schematic.
Ed