This is just a hunch, but this reminds me of Glasgow... where was it taken? Nice shots and welcome!
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I shoot wildlife (1Dx) pretty well exclusively, given the time frame you mentioned my suggestion would be the 70-200 f/2.8 V2 with a 1.4x & 2.0x extenders, keeps the weight down and gives you versatility (try to get the V3 extenders, much better optically than the V2 units), I use the 300/400 & 600 V2 lenses as well as the 70-200 and find with all the large Lenses I still use the 70-200 around 50% of the time, with the 70-200 you can zoom in, attach the extenders where required, but with something like the 500 your pretty well stuck if you need to move back, often not an option and by the time you set yourself back up to get the full animal in the shot, the animals long gone, and although the 500f/4 is not a monster, you will note the weight when compared to the 70-200.
I own a 500 f4 USM IS (not II). It is an outstanding lens for wildlife but it is big and heavy. I've seen people hand-hold it but I don't think you are able to take full advantage of the resolution of that lens doing it. You'd need a sturdy tripod and ball head or Wimberley type mount. If you're flying, it might fit in the overhead in its case by itself.
The IQ however, is much better than the 100-400 or the 70-200 with a 2x teleconverter.
Have you considered buying a 100-400 versus renting the 500? For 2 week trip, costs may be similar and in the end you could either keep the 100-400 or sell it and get a good bit of your money back.