If you wouldn't then you should reconsider your investment philosophy.
To answer that question, you would do it in a heartbeat. The funding rate for term deposits in Australia is about 3.5%. You would sell your LNG shares, buy a 20 yr term deposit. Sell your 14% term deposit on a 3.5% cap rate then buy yourself $8.66 worth of LNG shares. Doubled your money overnight.
You've taken a myopic view from what I can gather around dilution only and are failing to apply the principles of cost of capital, the use of funds and the importance of having a balance sheet and the effect this may or may not have on the progress of the company.
This table will help you understand how purchasing a portion of the equity stake from Stonepeak by paying for early works is in fact beneficial for shareholders as long as they spend at least circa $100m on it.