I have been struggling to decide between the 70-200 2.8 IS II and the 70-300 L. I do mostly portrait and family shots in outdoor/indoors and low light. I use a 5dII so I too think the 70-200 is very versatile for this body with the large aperature and still fairly wide on the FF. I will also plan to use the 2x III TC for the more limited times I shoot wildlife. Based on the images you posted it appears this combo can still capture plenty of detail. I figure this way, I get the best tele zoom while still having the flexibility to get the reach.
Does this strategy make sense to everyone?
Makes sense to me, and for portraits, I'd definitely pick the 70-200mm f/2.8L IS II over the 70-300mm f/4-5.6L IS.
Good example of the use case you describe was an outing to the zoo with my kids, where I took the 5DII and 70-200 II, along with the 2x II. The latter came in handy for shots of the animals, and even f/5.6 (on FF) is sufficient to blur out the fences reasonably well:
Thanks for your response Neuro. The color looks great on that last bird shot. As much as I like the form factor on the 70-300L, being able to take off the Extender on the 70-200 IS II and having a f/2.8 that is super sharp wide open means the lens has much more flexibility. In many ways acts as 2 lenses in one, given the IQ with the extender is still rather acceptable, which justifies the combined extra $1k you spend.
One side note to anyone considering the 70-200 f/2.8 IS II's weight (a topic that comes up on this and other forums almost daily!!).
When I first borrowed this lens from a friend, I ruled it out right away due to the weight, which after carrying it in hand for 30 minutes, I considered to be oppressive.
However!! The second time I borrowed it, I had purchased a Custom SLR Strap, a sling style strap with the glide feature(similar to the BlackRapid) and I was able to easily carry the lens with my gripped 5D Mark II for four hours with absolutely no fatigue. Plus you can easily move it behind your back and have your hands free for other things, in my case, namely my kid!
Long story short - plan on buying a sling style strap with the glide feature aka BlackRapid or Custom SLR strap(which I highly recomend). The weight issue quickly becomes a non issue, and you are left with one of the sharpest, most versatile lens out there (next to my 35 1.4L that is!!

)