Black Beard Algae PROBLEM

I need to eliminate the algae in my tank. I have been able to cut back
the lighting and to control the stuff on the glass. However, black
beard algae is growing on my gravel. I tried removing the affected
pieces but it comes back. BTW, I have a UV sterilizer. Can I remove
all the plants (if they died its ok) and treat the tank with an
algaecide? Then after everything dies, I could run my diatom filter
with charcoal to remove the algaecide residual. Then re-plant.

Would this work?

Thanks,

Rico