I'm able to report success with a breadboarded RC circuit that measures and displays BT rise per minute. While my simple prototype has some minor issues, and is not terrifically convenient to lug out to the roaster in its present state, I am satisfied that the basic design is good and can be effectively applied.
For convenience, I used a
Fluke 80TK adapter to amplify the raw thermocouple signal. This could just as easily be done with one of the several IC's available for this purpose.
The 80TK outputs a signal, in millivolts, equal to the temperature sensed by a type K thermocouple. I took this millivolt signal and ran it through a very simple
differentiator circuit comprised only of an op amp, capacitor, and resistor.
For the prototype, I used C = 1000uF, and R = 60k ohms. This gave me a direct readout in degrees per minute on the millivolt scale of my DMM. I had expected that the displayed rise / min values would have too much noise to be of use, but I was wrong. Even without doing any filtering, the blue line in the graph below shows that the rise / min values are fairly smooth.

In the above graph, the blue line represents the values of rise / min that were derived from the differentiator circuit and displayed on the Fluke 189 DMM in real time. The red line represents rise / min values that were computed, post-roast, using the temperature profile that was captured during the roast.

The above graph is just a simple record of the roast temperature profile. The blue line is the environmental temperature, and the red line is the bean temperature. These data were recorded on a Fluke 54 II.
Jim