Easy: bury the algae covered grains by turning the gravel layer over, then following with a water change.

Plants do not starve the algae, rather they remove things like CO2 and light and NH4 to virtually non detect levels in the water column.

Algae can sense that someone else is "there" by gene expression using NH4 as a signal or CO2 variation etc(which also can cause changes in the NH4 levels due to slowed or increased levels of NH4 uptake).

NH4 is rapidly removed in most aquatic systems and tends to be the main component to induce algae spores to germinate. If the spores are no longer germinating, then you have the algae beat.

Even at very high levels of NO3, PO4, and K+, traces etc.

The terrestrial ferts have lots of NH4, which is why they cause algae and should not be used.

The NH4 cation plays a large role in our tanks and explains why we cannot keep adding more and more fish to supply all the N for a higher light CO2 tank without getting algae.

CO2 demand and processing regulates NH4 uptake as well.
So it's a compounded interaction most likely.

Regards,
Tom Barr