SoftwareSerial 7-E-1 problem

Yes, I would try that one. The SoftwareSerial does work in some cases but in my experience it produces more problems than it solves. Most people new to Arduino think they can just replace a missing hardware serial with the software version but this usually doesn't work. The hardware version does a lot of stuff not possible in the software version because it would need more processing power than the ATmega series does offer (just one example: timing adaptions based on the received bits).
The SoftwareSerial does work OK for me up 38400 baud if connected to the PC (debugging) but with sensors and other devices I had success only with 1 in 7 cases yet. And even that one case required additional software checks to eliminate the occasional failures.