I built this op-amp circuit that takes in 4 inputs and outputs 3 sums by using op-amp adder and difference circuits to achieve a gain of 2x. In a simplified circuit, I boiled it down to the bare op-amps being used for the circuit in this image in an effort to show what I'm trying to achieve.
When I ran this circuit in LTspice, sending small inputs results in expected outputs. For instance, I sent in a 100-mV peak-to-peak sine wave (500 Hz) in at input A (while setting other inputs to ground), and I get a 200-mV peak-to-peak sine wave at the outputs. Furthermore, the output signals don't seem to affect the previous op-amps in the chain. (i.e., when putting a signal into A, the resulting output from OA6 does not affect OA5).
However, when I tested my circuit in real-life on a PCB, the results are strange, specifically when it comes to inputting a signal into C and D. When I input a 100-mV sine wave signal into A and B (again, 500 Hz), I get the expected 2x sine wave outputs. However, when I put in the same signal into C, I get a 3x gain instead of a 2x gain at output 2 from OA7. Furthermore, when analyzing the circuit when inputting the signal into D, somehow OA4 outputs a tiny 50-mV sine wave even though A and B are grounded. I think that somehow, part of my output signal is being fed back to the op-amp unintentionally which causes excess gain and strange signal outputs. What can I do to isolate each op-amp circuit so that they don't affect one another?
EDIT: I posted my rough, simplified schematic in circuitlab and showcased my entire schematic from my CAD software. To be clear, my op-amps have a potentiometer in parallel with the feedback resistor, but on the board, I only have one. I just made room for the potentiometer for troubleshooting purposes here; in case the gain was an issue, I could remove the fixed resistor, put in the pot, and adjust the gain to my liking. Regarding the offsets, I'm using a potentiometer to control them, but from what I saw, they don't seem to be a big issue. The voltage at the offsets should be very close to ground in the single-millivolt range or less.
EDIT 2: So, upon observation, I think that the issue stems with the difference amplifiers. Somehow, when I inject my test signal into D, OA4 outputs a small sine wave, even though A and B are shorted to ground. Perhaps this is what is causing all my problems, as all the problems seem to stem from the difference amplifiers. Why does this phenomenon occur and what can I do to prevent this 'feedback'?
EDIT 3: As requested, below is a picture of my 4-layer board. While it doesn't show a ground plane, rest assured that there is a ground plane present. It's just not filled in order to show the traces. I tried my best to add some silkscreen so that you can see the traces and follow along as best as possible. The left side has the inputs while the outputs are on the right side. Each input goes through the appropriate low-pass filter circuit as well as a diode clamp. From there, you can see how the traces are routed to each op-amp as per their scheme. The silkscreen makes each component identifiable, but it may be hard to read given the trace overlaps.