Thanks to a tip from Patrick of Pololu, I have figured out a second solution that uses this sensor in a non-blocking way. See picture below:
Basically, check first if new data is ready with Line 85, then do a non-blocking read(false) with Line 87. This "unblocked" Serial2 also.
For reasons still unknown to me, using read() in blocking mode (Line 89) somehow made Serial2 (created via SERCOM) "unavailable" in the remainder of my sketch. But if I use the BLE SPI module, with the first solution shown above, I can read these sensors in "blocking" mode! 