.High Speed is an adaption of the second book as Free is Utsumi spirit of the books ageing them etc. The Recap films show me the new director captures Utsumis vision very well and DTTF isnt as good as S2 but its more "Free" than High Speed. As admittedly yes High Speed is the best product because Takemoto does his standard fare that most people love but it is jarring to go from the OVA of S2 to that like I did last year it was a tonal shift. DTTF also adds High Speed elements through flashbacks but that is more because of like the Friendship angle that was basically S1 and most of 2.
The Major in the books reappears in episode 13 when Violet sees his brother in the house with Gilberts mother in the books its Gilbert so they have adapted that bit