How can I convert my U.S. dollars to Bitcoin and then invest in U.S. stocks from that balance—can this be done via a broker like Thinkorswim?

Not sure (at present) if you can use Bitcoin as a direct payment instrument for investing in US stocks. No broker/dealer, to the best of my knowledge, is accepting Bitcoin (without converting it into fiat first), and trading US Stocks.

I don't think the SEC would allow this.