Looking at what you've written, I'd write it up like this:
\m \v 1 A Psalm of David.
\p The LORD is my shepherd,
\q2 I shall lack nothing.
\q1 \v 2 He makes me lie down in green pastures;
\q2 he leads me to the waters of rest.
\q3 \v 3 He gives my soul new strength;
\q2 he leads me in the path of righteousness for his name's sake.
\q3 \v 4 Even when I walk in the valley of the shadow of death,
\q4 I will fear no evil,
\zq5 for you are with me;
\zq6 your staff and your rod,
\zq7 they shall comfort me.
You would probably have to use custom.sty to redefine some of the features of \q1-\q4, since they wouldn't look as you'd expect. And you'd need to also define new markers \zq5-\zq??? there. Of course, you'll also want to verify that whoever is going to typeset your Bible will agree and follow your new markers (see the rest of this reply).
But, I'd also push back extremely strongly on "There are at least 15 levels of indentation in the project." Why? Have you considered how this will actually look in print?
1) A lot of funders for the actual printing of books have strict rules on how Bibles should be laid out because they want to be economical. Thus their rules tend to promote saving as many pages as possible. This means small fonts, short indents, and as little white space as possible.
2) Even if money isn't an issue, I think what you're proposing above would look quite ugly in print and I'm willing to presume and to say that I'm speaking for most typesetters when I say that. That sort of waterfall with lots of blank space below it doesn't look nice and I'm not convinced it would aid in understanding.