A King's Pawn Opening Indian Defense
If I were to look at an opening system and count up advantages and disadvantages say, 10 moves in, and under "advantages" you'd have things like mobility, equality in space, king safety (o-o or ability/readiness for), the usual things a guy strives for either as black or white, I don't really see anything for black here except that it is not going to be white's favorite Sicialian position. There is some value in not playing "book" but that has to be balanced against the actual objective value of the positions generated.
The idea was to use black's ideas in the indian defenses of allowing white to take the center for a moment while black complete's development, then counter-attacking in the center
In that case a Pirc (1. e4 d6 2. d4 Nf6 3. Nc3 g6) or Modern (1. e4 g6) is probably what you are looking for. The Owens 1. e4 b6 2. d4 Bb7 is playable, but not very good.
An idea for a response to 1. e4 is Nc6, looking to set up a modified queen's Indian defense with 2... b6 and 3... Bb7. counter-play comes from an e6-d5 pawn break, and just using the main KID (King's Indian Defense) ideas, just mirrored. the one downside is that castling is a bit more time consumig