I can't emphasize this enough: like Yoda said, "Do, or do not. There is no 'try'".

With algae, if you're not winning, you're losing. Do NOT sweep till the water is gray. Do NOT be conservative in how much chlorine you add. (But, do not dump chlorine powder on the liner, unless you want a bleached liner!). Do NOT let it be green!

"really light green" = You are LOSING! You will be very unhappy, if you personally discover how fast established algae can re-grow, rendering all your work to date pure wasted effort. Add chlorine till it's gray, THEN clean and sweep . . . and add more chlorine!

The amount of chlorine needed to clean a swamp is HUGE. If you have the valves to do it, vacuum piles of algae sludge to waste.