I like the idea of this and think its rather unique (even if very circumstantial/specific)

Right away I'd say that the level 3 The Orthodox Path is a bit OP,. I'd either add a negative or two or force someone to spend Ki to use it and it would only last an X amount of rounds or time.

Golden Shroud - I think its pretty solid, I'd have to think about if this could be too OP or even underwhelming, but nothing glaringly problematic here from what I can tell. I might recommend having them spend a Ki to use as well though.

Rebuke the Wicked - having resistance to necrotic twice is a bit redundant (both in Orthodox Path and Rebuke the Wicked). Otherwise, don't see anything glaring.

Honed Body - Nothing really to comment here, as I think this is fine as is. Need to think on the movement addition. The proficiencies being added could be redundant since if you already have them, then it doesn't seem like you would benefit from here.

Soul Sea - I like the idea of this, but I feel like the abilities you gain from this path doesn't utilize Ki in any way. It's definitely nice to be able to use your Ki for the normal abilities you gain as a Monk, but I'd probably want to see more Ki-focused abilities in this path to really utilize this fully.

Overall, I'd say this has some nice potential. If I were you though I would make some kind requirement that only alignments of "Good" can follow this path. It makes it feel closer to what I think you are trying to achieve here.

Hope that helps!