Alright, silly me for just reading what's here rather than having a look around the UI and the files. There's another folder called digix_wdt which has the WDT-enabled version of variant.cpp named variant.cpp, and in the UI, there is a board choice labelled "Digistump DigiX (WDT enabled)"
I've also changed my setup code a bit to hopefully disable WDT so that it's only enabled after getting past a certain point in setup:
void setup ( )
{
WDT_Disable(WDT);
unsigned long wdp_ms = 2048;
unsigned long wst;
pinMode ( WiFiResetPin, OUTPUT );
pinMode ( LEDPin, OUTPUT );
digitalWrite ( WiFiResetPin, HIGH );
digitalWrite ( LEDPin, LOW );
ResetWiFi ( );
Serial.begin ( 9600 );
while( !Serial.available ( ) )
{
Serial.println ( "Enter any key to begin" );
delay ( 1000 );
}
Serial.println ( "Starting setup..." );
Serial2.begin ( 9600 );
WDT_Enable( WDT, 0x2000 | wdp_ms | ( wdp_ms << 16 ));
//...etc
}
Hopefully, that will stop any silly reboot loops because I've failed to connect to USB, open the console, and enter a character. Which should make it easier to re-program!