I'm looking to play through the game by pistol starting each map. I can see that this has been accounted for as each map has a shotgun near the player start. The issue is even if I kill myself I can't restart the level with just my pistol. I checked in the options and there's nothing. Anyone know how to do this?

The game was made to be played all the way through from start to finish. Different maps are connected together to form zones, which in turn are tied together by the parts where it states how many secrets you missed. Maps aren't meant to be played seperately. Because of that what you want isn't really a thing.

You could manually load the different map files from the console now that I think of it. In the console type something like: "map maps\z1a2" to open Zone 1, Map 2. It will automatically look inside the "fury.grp" file (kind of like an IWAD, but for Build games), but you do need to specify the "maps" subfolder like I did. The ".map" file extension isn't needed.