I believe we can very simply demonstrate that Jesus could not have sinned:
P1: Isa. 53, using the so-called "prophetic perfect" tense, which describes a future action as already completed in light of the certainty of God's decree, describes Jesus as having successfully completing His ministry, living a perfect life and dying a propitiatory death for the elect.
P2: God knows everything (1 Jhn. 3:19-20, Job 37:16, Ps. 33:13-15, 139:2-3, 147:5, Prov. 5:21, 15:3, Matt. 10:29, Acts 15:18) and it is impossible for Him to lie (Heb. 6:17-18)
P3: If it were possible for Jesus to sin, it would be possible for Isaiah 53 to have been a lie.
P4: But we have seen that it is impossible for God to lie.
C: Therefore, it was impossible for Jesus to have sinned.