I think the OP is getting close to answering his own question by suggesting that "superselection rules are just functions of our current technology." In my opinion, the answer is just a more precise statement of this suggestion: superselection rules capture beliefs we have about the nature of possible physical observables in the universe, limited by current experimental probes and theoretical models.
To explain that, we first give a mathematical definition of superselection sectors:
Definition 1: Consider a Hilbert space $H$ and a collection of subspaces $\{H_i\}$ such that: $H = \oplus_{i} H_i$. We say that $\{H_i\}$ are superselection sectors in $H$ if $\langle \psi_i| \mathcal{O}|\psi_j\rangle = 0$ $\forall$ $\psi_{i,j} \in H_{i,j}$, $i \neq j$, $\mathcal{O} \in O_{phy}$, where $O_{phy}$ is the set of all physical observables $\mathcal{O}$ acting on the Hilbert space $H$.
There are two important notions that have to exist a priori in this definition:
We have to specify a Hilbert space. To solve any quantum mechanical problem dogmatically, we would need a Hilbert space that contains states of the entire universe to ensure unitary evolution. However, practically, we often assume weak enough interactions between a test system $A$ and the rest of the universe $B$, so weak that we approximate $A$ as isolated (i.e. $H = H_A \otimes H_B$). So we can approximately obtain unitary evolution by restricting to the test system subspace $H_A$ for all interactions that act only on $H_A$. This freedom of choosing Hilbert spaces gives a bit of ambiguity to the meaning of superselection. Because it is possible that $\{H_i\}$ define superselection sectors in $H_A$, while $\{H_i \otimes H_B\}$ doesn't define superselection sectors in $H_A \otimes H_B = H$. We will see examples illustrating this later.
We have to define physical observables. Technically all self-adjoint operators on $H$ should be admissible candidates. But based on the current understanding of fundamental physics, we believe that certain self-adjoint operators are impossible to measure and certain transitions between states are impossible to engineer. Thus superselection rules today are practical tools that can be updated as we learn more about the world and find more physical observables that possibly break existing rules.
We now look at two examples to clarify why these two points above can cause confusion and to postulate a more complete definition of superselection rules.
Example 1: To illustrate the importance of the first bullet point, consider the OP's example of spins. Suppose we look at the Stern-Gerlach experiment and define $|\uparrow \rangle$ and $|\downarrow\rangle$ as eigenstates of the $\sigma_z$ operator. We take the Hilbert space $H_A$ spanned by these two states and postulate that the only physical observables on $H_A$ are $f(\sigma_z)$ where $f$ is some arbitrary analytic function. Now you may easily check that $|\uparrow \rangle$ and $|\downarrow\rangle$ define superselection sectors on $H_A$ alone!
But remember we have a freedom of choosing Hilbert space! Suppose now that we enlarge our Hilbert space to include a second particle $B$. Although we constrained physical observables on $H_A$ to be $f(\sigma_z)$, we don't have to constrain observables mixing $H_A$ and $H_B$. Even if we maintain conservation of total angular momentum $\sigma_z(A) + \sigma_z(B)$, we may well break conservation of $\sigma_z(A)$ or $\sigma_z(B)$ separately, thus mixing $\{|\uparrow\rangle \otimes H_B\}$ and $\{|\downarrow \rangle \otimes H_B\}$. This would imply $\{|\uparrow\rangle \otimes H_B\}$ and $\{|\downarrow \rangle \otimes H_B\}$ do not define superselection sectors on $H_A \otimes H_B$, as advertised in the first bullet point above. This is similar in spirit to OP's consideration of $p(particle) + p(recoil)$ on the Hilbert space $H_{\text{particle}} \otimes H_{\text{apparatus}}$.
Example 2: To illustrate the second bullet point, we consider OP's spin system without adding particle $B$. Instead we enlarge the set of physical observables by adding $\sigma_x$. In particular, we engineer a Hamiltonian $H= -\sigma_x$ by putting the spin in a unit of transverse magnetic field (as usual, we assume the interactions between the source of the magnetic field and the particle $A$ to be sufficiently weak that we can separate out $H_A$). Suppose we start the system in $|\downarrow \rangle$ at $t=0$, then at $t= \pi/2$, we flip the two sectors completely:
$$ e^{-i Ht} |\downarrow\rangle = e^{i \pi \sigma_x/2} |\downarrow\rangle = i \sigma_x |\downarrow\rangle = i|\uparrow \rangle $$
Again, as advertised, the introduction of more possible physical observables (in this case the introduction of $\sigma_x$ into the Hamiltonian) breaks the conservation of angular momentum and therefore the superselection sectors.
Example 3: Another example to illustrate the second bullet point. Let's escape from reality a bit more and imagine for fun that QM was discovered in 18th century, back when we believed in Galilean symmetry. To study states in QM, we found the projective representation of the Galilean algebra with $\{K_i\}$ generating Galilean boosts and $\{P_i\}$ generating translations. When we compose boosts and translations, we found that for a state with mass $M$:
$$ e^{-i \vec K \cdot \vec v} e^{-i \vec P \cdot \vec a} = e^{i M \vec a \cdot \vec v/2} e^{-i (\vec K \cdot \vec v + \vec P \cdot \vec a)} $$
This means a superposition of states with different masses would break Galilean symmetry, a sacred law of physics back then. In order to avoid that problem, we would have guessed a superselection rule forbidding transitions between states with different masses. And that rule would have stood the test of experiments and theoretical models up until the introduction of Einstein's relativity (which effectively modified the Hamiltonian, one of the physical observables, and its fundamental symmetries)! This is a rather dramatic illustration but I think it makes the point that what we call physical is always a matter of contemporary belief.
To summarize the discussion above, we come back to the classic example of electric charge. Why have physicists established the convention that charges define superselection sectors? It is because the superselection of charges is in some sense universal. While the superselection rule of angular momentum depends on the choice of Hilbert space, and the superselection rule of mass depends on choice of physical observables, electric charge is somehow different. As long as we believe in the Standard Model, no matter what Hilbert space $H \subset H_{\text{universe}}$ we choose (it can be the Hilbert space of the lab, of the earth, or of the whole universe), the subspaces $\{H_Q \subset H\}$ indexed by the restricted total charge operator $Q|_H$, define superselection sectors in $H$ in the sense of definition 1. Colloquially, this is to say: states with different charges don't talk to each other, for all choices of Hilbert space and physical observables within the Standard Model.
This last summary makes it clear that superselection rules we have today are intimately connected to contemporary beliefs about the character of physical laws. Maybe one day, there will be a new physical observable that mixes charge sectors, or a larger Hilbert space in which charge in one universe can be traded for charge in another. By that time, we would have to repeal the principle of charge superselection and hopefully find new superselection rules that will make our lives easier.
