Although transcendo might suit your purpose, I found that it was often used metaphorically not in the sense that you're speaking but more in the sense of exceeding moral boundaries, so your suspicion that it may be a false friend might be correct. Here's an example of it in the moral sense:
"Cupit regnum, et quidem scelerate cupit, qui transcendere festinat
ordinem aetatis, naturae, moris Macedonum, iuris gentium." (Titus
Livius, Ab Urbe Condita, 40.11.7)
With respect to transcending the limits of mind and body, the idea of ecstasis might be closer to what you're talking about, and there are a number of different ways to express that idea such as: "a sensibus alienari", "in mentis excessum rapi" or "a seipso discedere".
Here's some examples of usage of these ideas:
"Ergo non oportet propter hoc alienari a corpore vel rapi." (Bernard
de Trilia, Quaestiones disputatae de cognitione)
"Sed cum spiritalis visio, penitus alienato a sensibus corporis animo,
imaginibus corporalium detinetur, sive in somnis sive in ecstasi, si
nihil significant quae videntur, ipsius animae sunt imaginationes:
sicut etiam vigilantes et sani, et nulla alienatione moti, multorum
corporum quae non adsunt sensibus corporis, cogitatione imagines
versant." (Augustine, De Genesis ad Litteram, XII.12.26)