SO, I have concluded that the noise originates from the RCA input jacks, which perhaps are not grounded properly.

Although you are currently working on the right premise (narrow down connections and see if you can make the noise change as you alter the connections), I don't think you have enough information to support that particular conclusion yet.

Just because fiddling with the RCA connectors changes the amount of noise doesn't mean that they "originate" the noise. Although that very well could be the case, I think what's more likely happening is that there is a fault somewhere else the system (perhaps someplace completely different that's got a bad ground) and that touching/moving the RCA connectors increases their potential to ground and makes the ground loop worse.

Can you list each and every diagnostic step you've performed so far, including all wire gauges and connection points? Also, please list everything that you've already ruled out, and why. For instance, did you check for the rolloff capactiors? Listing that information might help us offer suggestions of things you haven't tried yet.