I'm not seeing TH on that shallow pitch at all really, especially as your tiles are terminating at an abutment, rather than being tucked conveniently behind say soffit or fascia etc. I suppose you could hide it with a lead flashing, but it will still look pants. We'd have likely cladded it with Cedral or plastic shiplap.
How are you dealing with the overhang? Regardless, I think you'll need to fill the battens with a solid run down the diagonal.
I just thing TH was a poor choice in this instance.
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