As a historic game based off of chu shogi, tenjiku shogi rule philosophy should by default defer to chu shogi rule philosophy. Taking the legality after each step, we only need to consider the final step for any multiple-step mover when evaluating whether it can promote. And since capturing a piece while leaving the promotion zone is a perfectly valid way to promote, this should be clearly allowed.
Edit: Now that I've thought about it a bit more, you should not be able to promote if: an unpromoted piece begins in the promotion zone, captures a piece in the promotion zone on its first step, then on its second step makes a non-capture.
As a historic game based off of chu shogi, tenjiku shogi rule philosophy should by default defer to chu shogi rule philosophy. Taking the legality after each step, we only need to consider the final step for any multiple-step mover when evaluating whether it can promote. And since capturing a piece while leaving the promotion zone is a perfectly valid way to promote, this should be clearly allowed.
Edit: Now that I've thought about it a bit more, you should not be able to promote if: an unpromoted piece begins in the promotion zone, captures a piece in the promotion zone on its first step, then on its second step makes a non-capture.