Brown algae is only one type most of us ,due to the amount of light for a turtle , have green algae to a point. The easiest way to control is to remove one of food sources it needs. We can't touch the light but CAN remove the nutrients it feeds on. Easy ways to control are : 1) feed your turtle in a separate container they are messy eaters. If done in the tank you may never find all the uneaten pieces thus nutrients for that algae. 2) Live plants will consume those nutrients better and faster than algae but does become turtle food. You would have to scoop up some broken plants but the brown algae will be gone. 3) Maybe a Pleco catfish could keep up with it.
By the way removing the light source as you did only helps Brown algae ! It's a low light algae. Maybe change placement of lights as long as it does not effect basking area temps. Now #4)Brown algae like's low oxygen , turtles breath out the water so no big deal here BUT low oxygen and Brown algae goes together . Live plants will help on that front to and a air stone with tiny bubbles helps to add oxygen also.
You have No water test kit ? Brown algae love high nitrates. For turtles best to try for (0) or around (10ppm and for me this # is high some may say little higher is still ok) My setup always below 5.0ppm but it's a lot larger than yours that makes controlling the water easier.
Also do not do 100% water changes or even 50% unless you have an big problem. How often do you do the changes and how much? You may have to adjust for that 55 gallon. I like 20-25% water changes more often at least once a week or less than one big one now and then. Works for me and I feed in the tank. This keeps your GOOD bacteria alive to help the tank !
What type and size UVA /heat bulb and UVB you have or maybe its a mercury vapor ? Brown algae come from low light , most of use see green algae do the amount of light for a turtle.
Here's a small read :
https://www.thespruce.com/brown-aquarium-algae-1378629