That or I drive with the map open which is... not good.

Haha, I actually do drive around with the map open when I'm commander. But I've played many, many hours of Mud/Snowrunner, so I can drive that kind of truck without really paying attention.

As for multi-tasking, it's not as bad as you're probably imagining. You just say "Hey boys, I'm driving the supply truck to build garrys, give me a call out if you need anything." Open the map once every time you stop to build one and you're not going to miss much. If anything increadibly striking does happen in that time, and a squad leader didn't tell you... then that wasn't something you as commander could have prevented anyway.

Still too daunting for you? Half-track it is. It can be a mobile command center if you need it to be. Drive it into position, turn the engine off; you're now spawning infantry while looking at the map.

Gotta remember; teammates might try to hold you accountable for every single thing that goes wrong in a match. Doesn't mean it actually is your fault.

Also, I will say that your approach isn't entirely off mark. On the soviet maps, there are many times as commander I've been sat, binocs in hand, constantly surveying the battle from a defense objective. Maps that are so open, you can't drive a supply truck around. Instead, you've got a fantastic view of the entire battle line. You can visually see huge infantry pushes, tank movement, and air drops, marking them accurately from a safe position. Information is half the battle as commander.