I think this is the best how to that ive found.
https://dcstructural.com/pdfs/technical/200706_from_experience_flitch_plate_beams.pdf
Seems like it wouldnt be bad to drop a pair of 1/4” plates between the sisters, but also unnecessary given the rest of the structure. Maybe iits a waste to pay the $150 to buy that metal.
this trellis thing isnt built with hangers. Blocking cross pieces are just casually banged together with pairs of 16d nails. Its designed to hold itself and some jasmine vines, and me abd my plywood when im washing the windows.