I'd be amazed if those HSERIN2 commands in your main loop work reliably
I agree with tumbleweeds thought, increasing baud rate to 38k cuts the time available to process that streamed data to one quarter of what was available at 9600 baud . its asking for trouble .
what possible advantage are you seeking with the higher baud rate ?
there is great merit in sending data to the serial display as fast as possible but I have difficulty seeing any benefit in getting nmea data at higher speeds.

now that you have a chip with adequate memory and horsepower why not use a buffer to store and process the sentences?