Welcome to the forum. I’ve now put in approximately 12acres of plots in our deep woods. Our soils are thin, very rocky, and very acidic because of the tannin in all the oak leaves. We started with plots in the low 4s PH wise and I learned very quickly lime was more important than fertilizer for getting our soil in shape. I’d start with buckwheat in the spring and cereal rye/clover/chicory mix planted labor day weekend. I’ve found that for October and early November, there is no stronger draw than grain. It may be with your milder weather, you can substitute oats and plant much later. Folks in milder climates may be able to say whether oats will have the same soil building qualities.
Regarding TSI, I think you will see far quicker results if you hinge cut. You’ll put literally tons of browse within reach, and you’ll thicken up quicker. We did 24 acres and it was a game changer for us. I confess I have no experience with burning (not allowed here) but getting a bunch of horizontally growing trees together with opening up the canopy will most certainly be quicker. It will make it so thick you’ll dread the day you have to drag a deer out of it….and thick is what you pictures suggest you need
Good luck on your journey and be patient. It takes time but is so worth it.