So on this forum there is the belief that Vader personally hunted down an killed every living Jedi, and also the belief that there were billions of Jedi.

Interesting.

Personally, I'm okay with the PT numbers. In the tens of thousands, maybe even up to a hundred thousand or so. Plenty to have enough to send in pairs or so around the galaxy to mediate hot spots when they deem it necessary, enough that people will have heard tales of their power and prowess in battle, enough for them to have entered into a mythological state, but not enough for everyone to have seen one or even believe the tales of their existence or powers.

I honestly never saw this as a problem. Of course there weren't enough Jedi to send one to every planet in the galaxy at a time, but not every planet is going to be experiencing turmoil requiring Jedi mediation at the same time, and not every planet falls within the jurisdiction of the Republic.