*very* long identifiability runtime for relatively small model

I have the following model:

ode = @ODEmodel(
    X'(t) = p - X(t),
    Y'(t) = -Y(t) + ((K1^3)*v1) / (K1^3 + X(t)^3),
    Z'(t) = -Z(t) + (v2*(Y(t)^3)*(X(t)^3)) / ((K2^3 + X(t)^3)*(K3^3 + Y(t)^3)),
    y(t) = Z(t)
)

for which the runtime of assess_identifiability is incredibly long. I.e.

assess_identifiability(ode)

takes at least 24 hours (I have not actually managed to complete it).

The model is essentially a incoherent feedforward loop (X deactives Y and activets Z, Y activates Z). In Catalyst it can be implemented like

rn = @reaction_network begin
    (p,1.0), 0 <--> X
    hillr(X, v1, K1, 3), 0 --> Y
    v2*hill(X, 1.0, K2, 3)*hill(Y, 1.0, K3, 3), 0 --> Z
    1.0, (Y,Z) --> 0
end

Reproduce assess_identifiability(ode) with the Julia model in the issue and measure where the runtime is spent. Read the implementation of assess_identifiability and its identifiability analysis path, using the supplied incoherent feedforward-loop model as the test case. Done means the example completes in a practical, documented runtime without changing its identifiability result.