If we agree that BJJ (Judo by another name) is a ground fighting system designed to defeat a single attacker on the ground,
Judo is not a ground fighting system to defeat a single attacker on the ground. It's about take downs and take down defense. Brazilian Ju Jitsu and Judo are both derived from Japanese Ju Jitsu, but they're only cousins.
A BJJ practitioner is going to have a very difficult time with a judoka, until the judoka gets a throw. If it's in an octagon or ring, the BJJ player pulls guard and works his game. If it's anywhere else, an ippon is probably a knockout or close to it.
Another notable difference is, judoka have to throw into a choke or hold almost immediately or the ref will stand them up. This is because on a battlefield, someone will come along and kick you in the head, etc. So you only get a few seconds to make a move.
BJJ players work a long game. Like wrestling an anaconda, you will succumb in the end if you fall into their grasp. The key is not to. You need good striking, good take down defense and you're right, Jonathan- you can surprise them with wrist locks if you are on the ground, but you have to immobilize them well- if they can squirm a little bit, they will wriggle out. Best take the opportunity to shoot your hips out and stand up, or land some crushing strikes- BJJ players do not like getting hit. Or have your friend kick them in the head, as you mentioned. That is their Achilles' heel.