I personally think it’s only a matter of time before a biologically plausible method is discovered
If there’s a lot of neurotransmitter still floating around the synapse, perhaps that results in a sort of weighted ‘forward’-prop that drags performance down the correct path, whilst the lack of it feeds back, so to speak, as a relatively negative ‘back’-prop — it’s not that back-prop happens as such but the forwardly weighted neurons fire sooner and, so, the less ‘charged’ connections effectively lose out in the competition to influence the outcome. 
The less influential inputs become even less positively weighted … resulting in an effective back-prop mechanism, albeit that it isn’t strictly back-prop as we know it in Comp.Sci. terms.
I’m being a bit vague … just musing really … but I could see it working that way.
 “Thanks for your input, but we’ve already found the solution.”