SoftwareSerial limitations - no bit-size, parity, or stop bits

The level of documentation is a frequently discussed item here.
As you have the sources of the serial you are invited to have a DIY party.

Easiest way to get 7-bit is to stuff the 8th bit with a 1 or a 0. might work like this

char c = 'a';
c = c & 0x80;
Serial.write(c);