How reliable do you want it to be ? Do you have a protocol to repeat messages ?
Doesn't need to be very reliable, the data flow will be one-way only, will be a number between +-90 degrees, and will probably not actually vary that much.
I can probably just slow the baud rate and do some error correction or averaging.
Yes, that would be the best option.
Between 1200 and 9600 baud, and a checksum byte.
How do you use the 6 wires ? I assume it is a flat cable ?
A ribbon cable has specific electrial characteristics.
You should decouple the power wires at the start and at the end of the cable. Or else a power peak might interfere with the data lines.
Perhaps like this:
1 = GND, on outside to avoid electric noise from outside.
2 = 5V, next to ground, because the current is 'paired' with GND.
3 = spare, perhaps for interrupt or data in other direction.
4 = spare, perhaps connect to ground at the transmitter size and open at receiver side
5 = DATA
6 = GND, on outside to avoid electric noise from outside.