The Sennheiser HD580s are 300 ohms, which is a great match for vintage amps, so I do not think the noise floor you're experiencing is due to the headphones. Any high impedance headphone 250 ohms and up, should sound great out of your JVC assuming the amp is working correctly and is connected correctly.This is some solid advice. I will definitly experiment more with the JVC in the chain. Perhaps a different set of headphones will be a better fit and lower the noise floor considerably? You mention AKG's. I'll see if I can pick up a used pair. That's always a risk-free way to try stuff out.
It could be that the JVC needs to be serviced, or perhaps how you're connecting your source to the JVC. Make sure you're running into the JVC in the AUX inputs in the rear, as opposed to the TURNTABLE inputs as they are not grounded , which will result in lots of noise.