Hi Russell:
Actually it would help a lot more if you gave the
exact specs of the all the lenses and bodies - for example what versions of the tele-converter you considering? There are two 100-400 lenses, and three 1.4 tele-converters, and we haven't even started on the potential bodies for compatibility with the tele-converters.
For what it's worth I use the Canon 100-400MkII lens with the Canon 1.4MkIII tele-converter on the 7DII or 80D body and it gives me excellent results but the auto-focus and auto-exposure don't work with other crop bodies that I have. Considering the FoV, that combination gives me a one Equivalent to that of a 224-896mm lens on a FF body - at which point IS is rather necessary and it's a bit of a howitzer. So I would put the 400 non-IS on the FF body and get the much improved aperture and the weight would be way lower.
Or you could sell one of the lenses and get the excellent Sigma150-600mm F/5-6.3 DG OS HSM Contemporary lens, which I also have and also gives great results.
Here is an image, as shot (i.e. no processing) of a heron at approximately 150m, hand held. It was taken with the Canon 7DII, using the 100-400 at 400mm with the 1.4 TC. (the EXIF data doesn't report on the crop factor effect of course). Even looking at it at full magnification on this site, it's nowhere near as sharp as the original, which is a pretty large image.