Well, I don't see why SoftwareSerial should behave differently from HardwareSerial as far as logic inversion is concerned, but you may try to initialize mySerial with a third argument, a flag indicating inverted logic. So you may try:
SoftwareSerial mySerial(rxMIDIpin, txMIDIpin, true);
(assuming this option was already implemented in version 1.0.1).
I would also remove the pinMode statements in setup(), which are managed by SoftwareSerial itself. Then I would try different pairs of digital pins, and would also measure their voltage, just rule out the possibility of different levels between pins 0, 1 and the rest.