7DII or 5d4 and 1.4TC; both of these work great for me, with my 'birding' preference going to the 7DII. I primarily use the 5D4 in reserve for landscapes and such while keeping the 'birding rig' intact for shooting.
That is a pretty tricky lighting situation, to begin with, and isn't an unexpected result, IMO, from the Tammy. They're great budget lenses, but they don't tend to keep up with the manufacturers' glass when conditions get tough. If you had microfocus adjust available through the lens range (kind of do with the dock on those newer lenses) and have that set up right, you could probably eke out slightly better results than that in those conditions, but I wouldn't take this single result or even an infrequent series of results like this as a need to upgrade. There are simply some conditions that won't result in shots you're happy with regardless of the gear you have.
Even with the above bodies and the 100-400II I have some days that net me these misses; sometimes AF just fails to find the info it needs to operate optimally 