You should be able to instruct your broker to basically use what liquidity you have to exercise one call (I believe there's no fee/commission to do that, at least not at my broker (ETrade)), sell those shares, now you have more cash to exercise more calls, ... and so on. They can do it for you, for a small (relative to 100 TSLA shares during a short squeeze) fee.
I had to raise some cash the other day and was faced with exactly this problem. I had some Jan 17 $100 calls, and they wouldn't sell even at their intrinsic value! I was just about to call the broker when a pop in the stock price caused the intrinsic value to go up enough to trigger at my limit, which was at that instant about $0.20 cents LESS per share than I would have made by exercising and selling at market.