Fish develop much more color and vigor with some sunlight. Keep up with good sized water changes.
Obviously the sun moves position all year long...how often is the sun directly shining through?
At my house I see some brighter sunlight coming through in fall/winter as trees leaves block some of the sunlight in other times of the year. I do not have an issue with the algae. I will see more of it than usual but the fish and shrimp do some work and then it kind of lessens and disappears when it gets more shade.
Also have used contact paper /film, in other times of tank keeping.
You could even put film on only the back of the sides leaving the sides still with vertical viewing from the front and front side. Or block only one side.
3M type film on the big house windows???
At the end of the day, trying the tank in the new location might work out and might not.
But if you like the tank enough to consider some creative options, trying it makes sense.
Does the sun come straight through the front of the tank?