With respect to conflicting rights, there are a number of methods adopted to address them. What follows is just my personal opinion. Of course, there are plenty of variables at play. For example, prioritisation of rights may depend on the source of said rights (i.e. constitutional rights vs. statutory rights vs international treaty-based rights vs. common law rights, etc).
For the purpose of simplicity, we may focus here only where rights exist within the same source (e.g. constitutional rights).
Firstly, of course, we need to see if there’s any specific interpretation of the clauses within the fact situation that allows us to retain each right without needing to resort to a trade-off. If such an interpretation is possible, then it should be adopted, even if it is not the “intuitive” or “common sense” interpretation.
If a harmonized interpretation is not possible, then it depends on the intended constitutional scheme: Is there an intended hierarchy of rights? If yes, then the right that is intended to be higher up the ladder dictates the extent of other rights lower down the ladder.
If there is no hierarchy of rights, then the extent of each right is in constant flux depending on the context and circumstances at play, and to deduce the correct conclusion, we need some kind of reference point to gauge when to limit one right in favour of another.
This reference point may well be a consequentialist one: what is in the best interests of the system governed by the constitution (in this case, PoH)? Whatever interpretation of conflicting rights secures those interests best should be adopted. Of course, there must be some general agreement on what the interests of the community are, too. Some may say maximizing the number of successful submissions is important, others might say that getting the “right” submissions is more important.
Alternatively, the reference point may well be a fundamental principle or value enshrined in the constitution itself; a kind of “summum bonum”. Traditionally, the job of a preamble is sometimes seen to express this value.
Of course, it goes without saying that any interpretation of the fundamental value should be an approach that protects all of the rights provided in the constitution as much as possible. If this is not possible, then one probably needs to adopt a thought experiment: Consider that both of the rights are completely and irreparably in conflict with one another in the specific fact situation before you. Which right’s absence do you reckon will destroy the purpose enshrined by the fundamental value (i.e. preamble) more? That’s the right that should take priority in the given fact situation before you.
It goes without saying that just because one right has been accorded priority as the result of a thought experiment, this doesn’t mean that the conflicting right can be ignored entirely; it must only be clawed back to the extent that the conflict doesn’t exist anymore. This may be referred to as the principle of proportionality.
Of course, I would recommend that this thought experiment should ideally be adopted for every single conflict that arises. The appropriate response in one fact situation may not be the appropriate one in another, even if the same two rights are in conflict and even if there are some similarities in the issues at play.
If doing the above requires a rethink of what you want the fundamental value to be, as prescribed by the preamble, then that may well be a sound investment of your time and effort.