Using a compiled function in NMinimize

Question

I can get NMinimize to work with compiled functions in simple cases.

This works with a constraint:

poly1 = Compile[{{x, _Real}, {y, _Real}}, x^2 - y x + y^4, 
  RuntimeOptions -> {"EvaluateSymbolically" -> False}]
NMinimize[{poly1[x, y], Norm[{x, y}] < 1}, {x, y}]
NMinimize[{poly1 @@ {x, y}, Norm[{x, y}] < 1}, {x, y}]

Or, a domain specification:

NMinimize[{poly1 @@ {x, y}}, {x, y} ∈ Disk[{0, 0}, 1]]

This appears to work, but the CompiledFunction warnings makes me think that the compiled function is not being used:

poly2 = Compile[{{x, _Real, 1}}, x[[1]]^2 - x[[2]] x[[1]] + x[[2]]^4, 
  RuntimeOptions -> {"EvaluateSymbolically" -> False}]
NMinimize[poly2[p], p ∈ Vectors[2, Reals]]

Another attempt didn't work at all:

poly3 = FunctionCompile[
  Function[{Typed[p, "NumericArray"::["Real64", 1]]}, 
   p[[1]]^2 - p[[1]] p[[2]] + p[[2]]^2]]
NMinimize[poly3[p], p ∈ Vectors[2, Reals]]

Can anyone see a way to get compiled functions to work with the domain specifications such as Element[p,Disk[]]?