I'm not even close to designing a double sided pcb for this! If it ever gets to that stage (and I am not counting on that happening) I will leave the design of the manufacturable device to professionals. I'm just building some devices (I've got 4 of them now) that I can work out some ideas.
The added display works nicely, but it's causing big problems for the radio. I moved the display device from the upper left of the board, above the antenna, to the lower right corner, and it still interfered:
The culprit may be the two 72mm leads that connect to the display module. When the display powered off, everything is fine, the radio receives the signal normally. As soon as the twi signal is turned on - even if the display is off, the interference starts. First thing I'm gonna try when I get a minute, is shorter leads. I would prefer to put the display back up above the antenna. But if that is not possible, I'll need to do some major re-designing of this device.
Another thing I need to do is change the way the output opamp and filter resistors/caps are wired up. Not for RFI, but for output impedance and current. You may notice I've removed some parts around the OPA4342.