I have never used a counter pressure bottle filler, so I can't help you there. However, I have used the Blichmann Beer Gun quite a bit. I think the point of purging the bottle is so you don't pick up or add any excessive oxygen to your beer when you bottle it. I have only used the purging option a few times, as I mainly only bottle one batch of beer a year, my big beer which is always bottle conditioned, so I figure in that case a little O2 would be fine.
As per your third suggestions, I've done both. I definitely prefer the picnic tap with a tub option over filling from the tap. I usually vent the keg a little so it doesn't foam, then start filling chilled bottles, that I want to ship to family. I only do this with beers that are going to be drank in the next week or two after filling, as how I do it, isn't really sanitary. I'd be overly worried about aging a beer using this process, without running cleanser and sanitizer through the picnic tap first.