Use of Codas without different endings and Voltas

I don't know if this is possible BUT -- I am trying to recreate a score which I have only in hard copy.

The score has simple repeats with no endings and then inserts a DC al Coda on the third repeat.
The score actually doesn't even have any repeat bars so I'm not sure how appropriate it is.

I have attached my working of it to Show what I am after.

Basically I want to go through a whole piece with different parts for alternating verses with leading voice changing.
So Part 1 of piece Verse 1 is followed concurrently by V2 then repeat to start V3 through V4 then repeat doing V5 to DC (where I now have first ending) back to start for V6 and to Coda (or Ending 4 as I have it.
The original Score indicates a DC al Coda only on the 3rd pass (after Verse 5) but I couldn't see how to make that happen. So I came up with Three different endings. First is full length of verse. That seemed a little clumsy but it works.

Is there a cleaner simpler way to do this? Can I in any way specify that DC al Coda only takes place on a 3rd repeat pass.