Serial.println(AcceX(ChipSelPin1));
becomes
int val = AcceX(ChipSelPin1);
Serial.write(hightByte(val));
Serial.write(lowByte(val));
You'll need some kind of separator between the pairs of bytes, so that if one gets lost, the receiver can know that and recover.
Or, you need some kind of separator between groups of bytes, and discard the whole group if the separator occurs again to soon, in the input stream.
Since you have no byte values that would not be part of the data stream, you have a couple of choices. One would be to split each byte into two nibbles, and send the 4 nibbles. Then, the separator can be any value over 127.
The other would be to send a series of (say 4) separator bytes (all the same value). That series of bytes is unlikely to appear in your data. That series of bytes could be 0s or 255s.