All in all, I'm a bit surprised it's the RX,Tx lines causing the problem, and not the 700-1000MHz oscillator signals getting into the receiver front-end. However, a simple 3dB low-pass filter is computed from F3dB = 1 / (2*pi*R*C), and 1Mbps corresponds to a 500KHz signal, so values of 330ohms and 1nF would round off the corners of the bitstream a good deal. So, you might try 100ohms and 1nF, or 220ohms and 470pF, or 1K and 100pF, etc. If serial becomes iffy [depends on the wire lengths], then use smaller values again.
EDIT: interestingly, a couple of years ago on the Arduino forum, they noticed a problem with the Rx pin on the DIP40 mega1284P chips. It's located adjacent to the OSC pin, and there was apparently cross-talk from Rx into the oscillator that disrupted operation. [note - only about 1/2 the people were actually seeing this problem]. The original fix put forth was to use a low-pass filter in the Rx line, but then they realized the bootloader chip fuse settings were using the low-power oscillator values, and they changed it to use the full-power oscillator settings, and the problem went away.