Edge choosability of planar graphs without 5-cycles with a chord

Let GG be a plane graph having no 5-cycles with a chord. If either Δ≥6Δ≥6, or Δ=5Δ=5 and GG contains no 4-cycles with a chord or no 6-cycles with a chord, then GG is edge-(Δ+1)(Δ+1)-choosable, where ΔΔ denotes the maximum degree of GG.