A rook sacrifice would have put you in a difficult position.
Unfamiliar opening
I don't now how to call the opening, but if you are interested in the white attack pattern (and how to defend against it), study the yugoslav attack against the dragon and the 150 attack against the pirc.

Thank you for the insightful response. What's the best way to deal with an opponent rushing pawns at your fianchetto'd position? (What would a better response on my part have been?)

Believe it or not , Richard Palliser calls it "The Tarzan attack".Leading d-pawn expert Eric Prie prefers the name "Vorotnikov-Kogan- Hebden attack" after it's 3 main exponents.It's not something to underestimate and it can be very complicated.For example ,
the following quick win from Hebden shows how easily this line can crush the unprepared.
Although I won the game through tactics, my opponent's rapid development looked peculiarly fearsome. I typically play KID against d4, but ended up improvising against the strange attack. What's the name of whatever white played? Was there a better response? In short, I hope to expand my opening repetoire to include whatever white did in that game.