Help reformulating nonlinear problem

Can you provide a fully reproducible example? What is model2?

What is not very close?

If I rename model2 to model, I get:

julia> @show dadϕ;
dadϕ = -1.5139167459828575e-7

julia> @show dadϕ_fdm;
dadϕ_fdm = ([-5.845569989199273e-6],)

That seems fairly close to me? (effectively, 0)