I think you may have multiple issues.
You will need to sort out either the control surface issues, OR the SID issues. Both might be related to the same problem.
I would probably say the SID issues are easier to resolve, because there’s less things to check, only one PCB where there might be a problem.
You can try the testtone app with the SIDs removed. This helps identify if there’s a problem with the audio buffers (i.e. the noise comes from them). Take out the SIDs and put a 1K (or similar) resistor between socket pin #8 and #27. Make sure you connect it in the right pins! Pin #27 will NOT have 9V! Connecting 9V to pin #8 is BAD
You should get 1kHz out of the audio outputs, this will probably be at max volume level too. If you don’t, there’s a break between pin #8 and the PIC, OR the audio buffer is the problem. You can narrow this down by connecting pin #8 from the left SID socket to pin #27 of the right SID socket (and vice versa).
BTW are you sure your audio is working? You are using a stereo plug?
The interconnection test is supposed to validate that the PIC->SID connections are correct, as well as connections to the two 74HC595 ICs below the SIDs. If you’re not getting the right voltages when you send the Mod wheel message to change which pin is high (for the pins connected to the 74HC595), then there’s some issue with the three serial data lines between the PIC and the 74HC595.
Check for bad solder joints, shorts, breaks, etc. between the PIC and the SID sockets, 74HC595 sockets.
AFAIK a high noise floor might result from either the audio input not being grounded (some issue with the audio input socket, or tracks between there and the SID pins)… OR if setting the volume registers in the SIDs isn’t working, because the data lines aren’t working. So until you get the interconnection test working properly, I would say not worry about high noise floor, that might be fixed by fixing the interconnections. Also, if you are still observing high noise floor when SIDs are removed, then it obviously has nothing to do with SIDs or the interconnections… some issue with voltages like the 9V supply, or ground, or the audio buffers. Try to identify if the noise is on one or both channels perhaps.