In terms of what you call 'equivalent' practices within the Gelug tradition, there's Mahamudra.
But they are not the same. They are said to have the same view, but divergent practice.
Dzogchen itself is practiced by people belonging to all the lineages. Among Gelugpas, it is not only
some eccentric interest of His Holiness the Dalai Lama, it is an interest of many Geshes.
Just as practitioners from all orders do choose to study at Gelug Universities, Gelug practitioners
often study at other colleges and with lineage masters outside of their main tradition. I know of
one Geshe from Sera, for example, who studied extensively at a Bon College. Another Geshe from
Ganden, studied Dzogchen with his father... it is not unusual.