@8bitDev: I'm sorry, but that really isn't good enough ...
Firstly, my iMX6 Droidbox behaves impeccably when connected in exactly the same way to exactly the same TV:
a) When it's "HDMI auto-output mode - Auto-match best TV resolution" is ON, it correctly recognises 1080p @ 60Hz and sets its "Output mode" resolution to this.
b) It preserves this "Output mode" (or, indeed, any other that has been set manually) across all shutdown/reboot cycles .
[Note that the T8, on the other hand,
incorrectly sets its "Output mode" to 780p @ 60Hz when its equivalent "HDMI auto-detection" is ON].
Secondly, your suggestion that 'the problem is in the TV' implies that, in spite of the TV accepting the correct resolution output signal from the T8 (ie that in force when the box was shut down) when it initially boots to the droidbox logo , the TV subsequently manages to instruct the box during its boot process that it must change its output mode to 720p 60Hz and that the T8 then obeys and stores this resolution as its 'Output mode' setting thereafter.
This seems to me to be an extremely unlikely, if not impossible, scenario but I would welcome a more detailed explanation than your 'somehow' above of the mechanism by which you think it may occur. Hopefully this will include an explanation of why the the putative instruction from the TV is issued precisely at the moment that the T8's output changes during boot from the droidbox logo to the animated 'spheroid'.
Personally, I suspect that a much more likely explanation is that the (presumably OpenGL) animation forces 720p @ 60Hz when it starts (either as a hard-coded value in the firmware or via its flawed auto-detection mechanism) and then 'forgets' to restore the previously-set mode when it is done. That's just my two-penn'orth but I would be interested to hear what, if you were to ask them, your firmware developers might make of it and/or any other comments they might have on the subject. In case it helps, my Android 4.4.2 'Build number' is: 'KOT49H.20150506 test-keys'.
My TV is a Panasonic AS600 series (Model no: TX-39AS600E) which does not have a facility for changing resolution when connected via HDMI and, like most modern TVs I think, passively displays whatever signal is input (including a blank screen for incompatible inputs).