The issue is that this is a matrix of vectors, which ForwardDiff doesn’t know how to easily handle. So it just gives you that matrix of vectors of duals (I’m surprised it didn’t error). [sol[LV.p]; sol[LV.V]] is a vector, and that should give a standard matrix Jacobian that would then resize.
For reference:
julia> a = [1.0,2.0]
2-element Vector{Float64}:
1.0
2.0
julia> b = [3.0,4.0]
2-element Vector{Float64}:
3.0
4.0
julia> [a,b]
2-element Vector{Vector{Float64}}:
[1.0, 2.0]
[3.0, 4.0]
julia> [a;b]
4-element Vector{Float64}:
1.0
2.0
3.0
4.0
julia> [a b]
2×2 Matrix{Float64}:
1.0 3.0
2.0 4.0