Guenon gives precise definitions and parameters of syncretism and synthesis within his book "Perspectives on Initiation", Chapter 6, Synthesis & Syncretism such that it is sufficient simply to refer to this source for clarification.
According to Guenon, "Syncretism in its true sense is nothing more than a simple juxtaposition of elements of diverse provenance brought together "from the outside" so to speak, without any principle of a more profound order to unite them." The two primary examples that he gives are "Modern counterfeits of tradition like occultism and theosophy ... fragmentary notions borrowed from different traditional forms, generally poorly understood and more or less deformed ... mixed with ideas belonging to philosophy and profane science." These represent practical and doctrinal syncretism respectively. Aleister Crowley's occult order Astron Argon (A.'.A.'.) is an example of the former. Practically, it combines elements of medieval, renaissance, and modern ceremonial magic with different forms of yoga as expounded by Swami Vevekananda, and psuedo-Egyptian initiatory rites, within an improvised framework of Kabbalistic symbolism. For an example of the latter, which is chiefly doctrinal, one can simply peruse either of Blavatsky's primary theosophical texts Isis Unveiled and The Secret Doctrine.
Also according to Guenon, "Synthesis starts from principles, that is to say from what is most interior; it goes, one might say, from center to circumference." Guenon's chief example of synthesis is the metaphysical exposition of traditional doctrine. He states that "Whatever is truly inspired by traditional knowledge always proceeds from "within" and not from "without"; whoever is aware of the essential unity of all traditions can, according to the case, use different traditional forms to expound and interpret doctrine, if there happens to be some advantage in doing so." A good example of this is Schuon's alternate use of Platonic, Hindu, and Islamic equivalent terms when expounding metaphysical principles.
Guenon here emphasizes doctrinal synthesis but does not mention practical synthesis although we do know from prior comments that traditional ritual practices are inherently incompatible at the formal level. One practical domain in which synthesis seems plausible is that of the cosmological sciences such as astrology, alchemy, and architecture. The unifying element in this case is the cosmological vision underlying the science which may be transposed into various traditional domains and exposited within the language of the respective revelations with which it becomes associated. One may examine the Codex Rosae Crucis D.O.M.A., for example, which is a magnificent representation of Christian Alchemy, while remembering that the alchemical art passed into Christendom, through the Islamic tradition, which in turn inherited it from the Graeco-Egyptian tradition. Alchemy may be exposited in distinctly Christian terms, and related to from within the scope of the Anthropocosmic vision of Christianity, but the science remains internally consistent from "within" different traditional domains ...
Alchemy is fundamentally the science and art of the transmutations of the soul leading to the restoration of the perfection of the human state. Although its primary aim is the inner transformation of the alchemist, its outward supports may vary to include all traditional arts and crafts, especially metallurgy (which provides the fundamental basis of alchemical symbolism) and architecture (which has served as one of the primary vehicles for alchemical symbolism), prayer within an overtly spiritual alchemy, and the subtle centers of the body (which, although they are engaged inadvertently through any spiritual method, may also serve as a direct focus and operative support of concentration).
Although the language of alchemy is diverse and convoluted, often possessing subtle variations according to the individual alchemist endeavoring either to explain or veil the nature of the practice, it is internally consistent such that its basic themes and perspective may be reasonably communicated. Therefore there are a number of very clear contemporary writings on the subject not least of which are the chapter on Alchemy in Seyyed Hossein Nasr's Science and Civilization in Islam and Titus Burckhardt's Alchemy: Science of Cosmos, Science of Soul, this latter of which may perhaps be considered the final word on the subject in terms of contemporary expositions.
You ask, "how can one integrate a pursuit/study of alchemy with a general Islamic/tasawwuf orientation? I presume it's been done before, since I've come across many references to alchemy in the words of the sufis themselves..."
There are essentially three ways to do this correlating to the operative supports mentioned above: learning the interior dimensions of a craft from a traditional artisan, contemplating alchemical symbols to gain additional insight into a spiritual method, and directly incorporating the subtle centers of the body into the method. Each of these possibilities requires qualified guidance for improvisations never enter into the domain of orthodoxy.
In the first instance, a bond exists in the Islamic world between the traditional craft guilds and the orders of Sufism. With the rise of industrialization and the loss of traditional crafts, this possibility is more remote than in previous centuries, especially outside of the Islamic world. I have only ever met one craftsman, a blacksmith, in Southern California who claimed knowledge and practice of the alchemy of his craft, though his traditional filiation was questionable.
In the second instance, prayer, especially invocatory prayer, serves as the operative support and the verbal symbol a means of grace - Its permutations within the soul correlating to the various stages of alchemical transmutation. Al-Ghazali identifies four principal stages of invocation and specifically refers to the last as the Alchemy of Happiness and ultimate aim of the spiritual life, when the love of God overcomes the love of the world and the invocation takes possession of the soul. All Sufi orders teach a spiritual method correlating to this, though not necessarily in Alchemical terms in which case the contemplation of Alchemical symbolism may add an enriching point of reference for deepening one's understanding of the interior processes accompanying the method.
Finally, there is the consideration of the implementation of the subtle centers of the human body. Just as the spiritual archetypes present within the celestial realm as the planets manifest within the mineral kingdom as the metals, the interior analogue of these archetypes within the human microcosm are the subtle centers which are the domain or seat within the subtle body of various faculties. Concentration upon these centers in conjunction with the invocatory method corresponds to that phase of the alchemical work sometimes referred to as the embodying of the spirit which follows the spiritualization of the body. Many Sufi orders, including the Naqshbandiyya, Chishtiyya, and Shadhiliyya, integrate this form of subtle concentration into their spiritual methods.
These then are three ways in which an inclination toward alchemy can be pursued within the domain of Islamic esoterism.