Yes, as mentioned by Big Uncle, I have read it too that because Drakpa Gyaltsen's fame rivaled that of the 5th DL, Sonam Chopel and some other DL's other attendants became extremely jealous and later murdered Drakpa Gyltsen.
Like most of you had mentioned Desi Sangye Gyatso is a High Lama and have done many great work. Surrounded by his lineage of previous incarnation including Vajrapani, Arhat Anirudha, Dharmaraja Chandrabhadra, Arya Asanga, Tsunmo Yiongma, Gyalbu Gawai Pal, Drangmo Dema, Trulpai Tachog Changshe (Horse), Dharmaraja Bhanga, Khyeu Gyuma Chilwa (Parrot), Khyimdag Palbe, Lonpo Netso Yuting, Lhase Mutri Tsanpo, Trinyen Zungtsen, Gungru Gungtsen, Mune Tsenpo, Lhalung Palgyi Dorje, Drubtob Nyima Dzin, Ngog Legpai Sherab, Drupai Wangchug Ratna Lingpa, Sechen Chokyi Gyalpo, Terton Zangpo Drag, Kedrub Norzang Gyatso, Altan Chokyi Gyalpo, Mize Sangye Gyatso (1653-1705), Je Konchog Wangchug, Tala Ngagwang Palzang, Lharampa Zopa Gyatso, etc.
Je Konchog Wangchug was recognized by the 6th Dalai Lama as the Desi incarnation and the line continues to this day in Mongolia.