[netmgr], who has similar hardware, realized why I was having trouble with the humidity field. It's not just one field, it's three separate fields that affect humidity! I believe they are two coefficients (I'll call them a and b), and a value. The dummy coefficients I had been sending had resulted in a nonlinear response to changes in value.

Armed with that knowledge, I started adjusting the other values as well. Plugged in a=b=100, sent a range of inputs to the value field, and plotted a (linear, this time) regression in a spreadsheet. Result:

Humidity is expressed as 500 * (161*percent + 1234) / 1983. 

It may not seem like much, but it was the last "stumper"!