Wow Jake! These are both excellent shots!! And stacking two 2.0 TC's are amazing! Hand held or on a tripod? I am thinking tripod because of the weight of the 300-800mm.
I am guessing your TC's are of the Canon brand, although I thought I had read a while back that Canon TC's were also NOT stackable.
When I bought my Sigma 150-600C I bought the 1.4 and 2.0 both Sigma brand but sadly found out those are not stackable.
Of course tripod! And even on a series 4 with a full Wimberley head, @ 3200mm even the slightest vibration made the moon move all over the screen!
The two 2X T-Cons were either one of the OEM Sigma made to go with this lens, or the Canon MKIII, (I can't remember actually, but I think it was the Sigma) and a Canon 2C MkII which was in fact designed to allow stacking. It is the only one that was,. and I kept it for that reason. So any t-Con, 1.4x, or 2x, Canon or Sigma can be stacked behind the Canon MKII.
The only other 2X T-Con that I seem to remember reading was stackable is Kenko, but I might be making that up.