I just want to make sure it's not the glass. I don't know your experience level, but if you own a 5D3 I must presume 1 and 2 above are not the problem. 
i was shooting for 12 years with pentax.
but as pentax is going nowhere as it seems i switched to canon this year.
i have what i need so far (70-200mm f2.8 IS II, 50mm f1.2, sigma 35mm f1.4)
but im struggling to find a really good 24mm (my prefered focal length).
i buy fast glass when i think i need it.
but for my 24mm work f2.8 is fast enough.
so i prefer not to "waste" money in this case, if i don´t have too.

if there is nothing for 800 euro that is as good as the EF 24mm f1.4 L from canon, then i will buy the EF 24mm f1.4 L.
but i think the 24mm f2.8 IS is maybe pretty close?
i mean it´s a new design.
How much are you willing to spend. Not necessarily your "budget" but the absolute maximum you are willing to spend. Good 24mm is going to cost $
as much as i have too.

but it does not have to be very fast glass.
it only has to be sharp and distortion free.
the 24-70mm f2,8 IS II is sure a great lens but costs 2000 euro.
i am not willing to pay that only for the 24mm end. i have a good 35mm and 50mm lenses already.