I currently have a D4s and a 400mm f/2.8 FL ED VR and almost always use it with the TC-14E III. I find myself almost always cropping 100% or more to get the desired composition for most of what I find myself photographing. (Surfing from shore).
I'm intrigued by the slight resolution increase of the D5 and am not too put off by the less flexible dynamic range. I'm very interested in the increased sensitivity of the center AF-point as I almost always toggle between AF-C dynamic 9 and AF-C single point (via the customizable buttons on the lens barrel).
I love compression and the long-glass look and always shoot wide-open. Granted the price difference is huge, but life is short.
I think the 400 f2.8E FL VR + 1.4x TCIII will give you similar IQ to the 600 f4, there will be little in it. Personally, I would buy a D500 and use your 400 f2.8E FL VR + 1,4x TCIII when required. With the D500, you basically have a "600 f2.8 VR". The D500 has the same or very similar AF to the D5 and it is ligthing fast and accurate.
This is generally my birding set up, D500 + 400 f2.8E FL VR and use the 1.4x TCIII when required. Simply a brilliant birding combo! If I take my D810 along, I have a 400mm f2.8 bare and a 560mm f4 with the 1.4x TCIII and with my D500 I have a 600mm f2.8 bare and an 840mm f4 with the 1.4x TCIII.
View at full res.
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/800s f/5.6 at 560.0mm iso200
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/640s f/5.6 at 560.0mm iso360
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/800s f/5.6 at 560.0mm iso640
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/640s f/5.6 at 560.0mm iso1400
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/1250s f/5.6 at 560.0mm iso3200
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/1000s f/8.0 at 560.0mm iso1800
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/800s f/5.6 at 560.0mm iso3200
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/1250s f/5.6 at 550.0mm iso5600
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/2500s f/8.0 at 400.0mm iso2200
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/800s f/5.0 at 560.0mm iso280
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/800s f/5.0 at 560.0mm iso140
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/800s f/5.6 at 560.0mm iso160
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/2000s f/6.3 at 560.0mm iso250
D500 + 400 f2.8E FL VR + 1.4x TCIII, 1/400s f/5.6 at 560.0mm iso1400
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Lance B
http://www.pbase.com/lance_b