AD (Zygote, ForwardDiff) compatibility?

LabelledArrays looks very promising to simplify model definitions. Unfortunately it seem largely incompatible with AD. Is there a good workaround?

using LabelledArrays
import ForwardDiff
import Zygote

model(p) =  p.a + p.b^2 + p.c^3

p = LVector(a=1, b=2, c=3)
ps = SLVector(a=1, b=2, c=3)
model(ps)
model(p)

ForwardDiff.gradient(model, p) # works :)
Zygote.gradient(model, p)      # ERROR: ArgumentError: invalid index: Val{:c}() of type Val{:c}

ForwardDiff.gradient(model, ps) # ERROR: type SArray has no field a
Zygote.gradient(model, ps)      # ERROR: ArgumentError: invalid index: Val{:c}() of type Val{:c}

(In case of ForwardDiff this is probably related to #68)

Reproduce the Julia examples for LVector and SLVector with ForwardDiff and Zygote, then inspect the compatibility concern linked to issue #68. Compare the reported field and Val-index errors across both array types; done would require a confirmed compatibility fix or a documented workaround.