Yes, there is ample precedent for praying to both Christ and His Mother, not only canonically and thus discursively, but in the methodic, “hesychastic” way you allude to. I would recommend, however, that if you wish to use two full petitions, they should be: “Lord Jesus Christ, have mercy [adding, perhaps, “on us” or “on me”], and “Most Holy Theotokos, save us”. It is common Athonite practice to pray alternate ropes using first one and then the other of these two potent formulas.
On the other hand, an Orthodox case can also be made for combining these twin prayers in a single formula, reducing the petitions—at least in certain cases—to the two Names alone. We know, for example, that St Maximos of Kapsokalyvia, a fourteenth-century monk of the Holy Mountain, practiced what he called “the remembrance of Jesus and my Theotokos” [??? ?????? ?o? ???o? ??? ??? ??o???o? ?o?], and though we’re not sure of the precise form of his invocation, it must in some way have synthesized the full petitions just cited.
In The Living Witness of the Holy Mountain: Contemporary Voices from Mount Athos, the editor, Bishop Alexander (Golitzin), has included an anonymous selection entitled “The Garden of the Mother of God”. Referring to the Theotokos, the author speaks of certain monks who “join Her name with that of our Lord Jesus Christ so as to unite it with their breathing and make it descend into their hearts”. One notes as well that the Elder Joseph the Hesychast, in the collection of his writings entitled Monastic Wisdom, more than once speaks about invoking the sweet “Name” (N.B. the singular) of Jesus and Mary.
Of course, whatever the form of your practice, it should be undertaken only with the blessing and guidance of your spiritual father.