The PWM period of the sensor output signal is a whopping 1004ms!
At 64MHz the longest time you can measure with PULSIN is ~41ms. You'll only be able to measure at the very low end of the sensor range with that method.

There seems to be an analog output as well, perhaps you can use that if you're not able to get the serial working. Or lowpass filter the PWM signal as mentioned.

Your settings and command string does seem correct. The datasheet says "Users must use TTL level. If RS232 level, it must be converted." which to me means you should send data non-inverted (which you are). You could try sending it inverted as well, mode 16468 I believe. I'd be surprised if that's it but it's easy to try.

Sometimes the terms RXD/TXD gets mixed up. In this case the datasheet is pretty clear that RXD is the input of the device (as apposed to mean "connect to RXD on the uC). Do you have it wired correctly? Have you tried switching RXD/TXD?