How to graph search a LTL-generated Buchi automaton to generate valid execution paths
I would interpret your problem as follows:

Given a non-deterministic Büchi automaton representing some language $L$, you want to enumerate all shortest good prefixes of $L$ such that in every character of the good prefix, only at most one atomic proposition has a $\mathbf{true}$ value.

A good prefix of $L$ is a finite word such that every infinite extension of it is in $L$. I call a good prefix a shortest good prefix if and only if every prefix of the prefix is not a good prefix.
A schedule is typically finite even though LTL and Büchi automaton "talk" about infinite executions. Hence this interpretation of your problem.

Note that this is actually a difficult problem -- take for example two Buchi automata for the languages []&lt;>p and &lt;>[]!p -- you can take their disjunction by merging the state sets and having two initial states. You do not see syntactically that every word is a good prefix. 

The best way to enumerate good prefixes would thus be to construct a deterministic automaton over infinite words, such as a deterministic Rabin automaton, and enumerating all paths to a strongly connected component in which every state represents the universal language.

Enumerating the paths can be done by a simple depth first search, where you do not abort the search after you found a path to a state with the universal language. Whenever you found a path to such a component, you print it out, and return to the next recursive step. Along the way, you ignore characters with more than one proposition set.

Now in practice, you may have a good luck using LTL-to-Buchi converters. They typically do not guarantee that they find all simplifications of the LTL formula, but enumerating paths to accepting states may do the trick. Note that for non-deterministic automata, you can get duplicate schedules.
If you use modern tools for LTL-to-deterministic-automaton translation (such as Rabinizer), they should also make sure that states belowing to a strongly connected component for the universal language are self-looping on all characters, which makes them easy to detect. But I don't think they guarantee this.