I am currently trying to relax some finiteness conditions for a result I am trying to prove in rational homotopy theory (to avoid having the result holding only for the space given by a single point) and I find myself confronted with the following two closely related questions, which I guess have already been considered many times before. A reference to an answer to (one or both of) those questions - in the positive or the negative - would be extremely welcome.

1. Let $X$ be a simplicial set. If necessary, assume that $X$ is connected, nilpotent, and of finite $\mathbb{Q}$-type. Is there a "rational" fibrant replacement for $X$, i.e. a map $X\to Y$ that induces a quasi-isomorphism $A_{PL}(Y)\to A_{PL}(X)$ and such that $Y$ is Kan? it would be even better if this map were a weak equivalence of simplicial sets. Of special interest to me is the case where $X$ has finitely many non-degenerate simplices in every simplicial degree ($Y$ is of course allowed to have infinitely many).
2. Let $X$ be a Kan complex which is connected, nilpotent, and of finite $\mathbb{Q}$-type. Is $X$ always "rationally the same" as a connected, nilpotent simplicial set of finite $\mathbb{Q}$-type with finitely many non-degenerate simplices in every simplicial dimension?

Question (1) might be easy, maybe just taking any fibrant resolution or maybe taking the chains over the geometric realization of the space, but I'm not aware of the fact that $A_{PL}$ sends weak equivalences to quasi-isomorphisms (indeed, Bousfield-Gugenheim say that they suspect that it is not the case just after Prop. 8.3 in their article). I took a look in a couple of standard sources (Bousfield-Gugenheim, the book by Félix-Halperin-Thomas) but without success.