I have the 100-400 as well, but 400mm is not enough for me. Same problem with the 400/4.5 which has a 1.4x tc glued on it.
For me I think a 100-400 + 600pf would be the best combination (or 800pf).
Birds are very shy overhere. Most of the time I have the 1.4x tc on the 180-600 and that’s not the best option.
I plant to complement my 100-400 with the 600 pf too. The not so high weight of the 600 pf helps to have it along more frequently when a long lens is wanted. Otherwise I am happy with the 100-400 as a cover 'all' of tele range, it comes along on many of my not terribly long hikes. I might use the 100-400 + 600pf only from a vehicle on some sort of safari.
Since you, Chris, typically use 600+tc1.4 , I would think your use case calls for the 800pf . Contrary to the 600 pf, I judge the price of the 800 pf as expected, while the price of the 600 pf seems too close to the 800 pf for me, and very much higher than the 500pf, while the front lens size of the 600pf is the same as 500 f/5.6 pf or Z 400 f/4.5 .