Putting tax-free earnings in a TSP (or 401k, or traditional IRA) is pointless. You're not deferring any taxes, you have to pay taxes on your earnings anyway, and you're preventing yourself from touching that money until you have old balls. Just put that money in a brokerage account; it's the same.
The way that reads, it looks like you can't contribute to a Roth if you literally have $0 of taxable income (which I didn't know). If you still want to fund it, you might want to look into interest income (SDP is $1k to start) or capital gains.