Yes, currently BesoGo only natively supports displaying the full board. However, if you want to crop the board display, I think the easiest way would be to modify the boardDisplay.js file (as you already suggested). Specifically, see line 111, which sets the viewBox property of the SVG element to control which portion is displayed, and related calculations on lines 104-106.
Actually, in the related project Josekle (see Josekle 🟢⚪🟣🟢🟣), modifying the viewBox is used to adjust the zoom (crop). This is done in lines 531-538 of this file.