Resolution of pairs in characteristic p

Let $$R$$ be a complete DVR of characteristic $$p$$, say $$R=\mathbb{F}_p[[t]]$$, and $$X$$ be a reduced scheme of finite type over $$R$$. Let also $$X_s$$ denote the special fiber of $$X$$. If I understand correctly, resolution of singularities in characteristic p, says that there is a regular scheme $$X'$$ of finite type over $$R$$ and a blowup $$f:X'\to X$$ in a nowhere dense center $$Z$$.

However, it gives us no information on what the new special fiber $$X'_s$$ looks like.

Q: (a) Is there a (conjectured) version of resolution of singularities in characteristic $$p$$ that also ensures that $$X'_s$$ is of a "nice" form (normal crossings divisor)?

(b) If so, does this mean that $$X'$$ locally looks like
$$\operatorname{Spec}(R[x_1,\dotsc,x_d]/(f_1^{e_1}f_2^{e_2}\dotsb f_n^{e_n}-t))$$ where the $$\mathbb{F}_p$$-schemes cut out by the $$\bar f_i$$'s are as in the definition of normal crossings?

It seems that the corresponding statement in characteristic $$0$$ is true and well-known (Theorem 3.1.5 in Temkin - Absolute desingularization in characteristic zero). Also, any references that address this (or closely related) issues would be useful.

Some background: I am not an algebraic geometer, but I found it convenient to assume, at least temporarily, some form of RoS in characteristic $$p$$ for a problem I am trying to solve.