Although the absolute value of a digital potentiometer's resistance may vary 30%, the matching between the internal resistors is really good. This means that for a voltage divider (to wit, a potentiometer), the voltage division accuracy is quite good, since the voltage division factor relies entirely on the ratio of the resistors used, not their absolute value.
If your output voltage is less than the digital potentiometer's maximum voltage rating, you can simply use a digital potentiometer to stand in for the feedback network without any fanfare. Most digital pots can take only 5.5V, but some are rated for substantially more.
If your output voltage is higher than the digital potentiometer's maximum rating, or if you want fine adjustment, you can combine the digital potentiometer with external resistors to form a compound voltage divider. Note that this will cause the digital potentiometer's absolute value variation to come into play. Techniques exist to minimize this error, as covered here.
If you want to avoid digital potentiometers altogether, you can make the feedback divider take input from a D/A as well, as shown here by having a D/A drive \$V_{CTRL}\$:

simulate this circuit – Schematic created using CircuitLab
Since the feedback voltage \$V_{FB}\$ will be regulated by the LTC3780 to 0.8V, the output voltage will be regulated to:
$$V_O=\left(1+\frac{R_2}{R_1}\right)0.8-\frac{R_2}{R_3}(V_{CTRL}-0.8)$$
Setting \$V_{CTRL}\$ to 0.8V causes no change in the output voltage; increasing \$V_{CTRL}\$ causes the output to drop, and decreasing \$V_{CTRL}\$ causes it to rise.
It should be noted that no matter what you do, you should carefully evaluate the regulator and adjust components (\$L\$, \$C_{OUT}\$, \$I_{TH}\$ network) to ensure stability over all operating conditions. When in doubt, lean to the conservative side here.
IGBTs have high voltage drop and are not suitable for low voltage switching. They only exist because reliable high current high voltage MOSFETs are hard to make.
You should use high current MOSFETs rated at 30~40V. Maximum current is often package limited, but several FETs can be wired in parallel to increase current handling. For example the IRFP7430PbF is rated at 404A, but package limited to 195A. Rdson is 1.3 milliohms, so two in parallel should drop 0.13V at 200A (= 13W per FET). In comparison an IGBT module could drop 2V or higher, resulting in 400+ Watts of heat to get rid of!
The advantage of a module is less wiring and simpler installation. One disadvantage is that it's toast if even one transistor dies. Also an IGBT module may be much more expensive than a few discrete FETs.
Best Answer
I doubt that you really need 2 potentiometers in the first place. Keep the boost (first stage) at fixed output voltage. Control the buck (second stage) with one potentiometer.