Richard B. Hays has elaborated in various places helpful methods for detecting intertextual echoes in texts. The basic criteria he gives for doing so are the following (HT: Joel Garver):
 availability of the source text to the author and his audience,  the volume of the echo in terms of its explicitness,  recurrence or clustering of allusions or echoes from the same text,  thematic coherence with the line of argument,  the historical plausibility of finding an intertextual reference given the original situation,  the subsequent history of interpretation finding the echo, and  the satisfaction given by the intertextual reference in reading the surrounding text.
For the second criteria, there are three sub-criteria:
[a] verbatim repetition of words from the source text, [b] the distinctiveness, prominence, or popular familiarity of the precursor text, and [c] the rhetorical stress placed upon the phrase in question
While one can dispute individual uses of these rules, I think it is fair to anticipate that the authors of the bible would be capable of allusion, and thus I think it is reasonable to use these in our interpretation.
Further, it is a general rule of interpretation that we interpret the words of an author in the context of what we know about them in general, especially including other things they have written (especially the immediate literary context of the text).
But, as Vern Poythress has explained in detail, whenever we read scripture (and if we believe it to be inspired), we have to reckon with two authors, not one. (And further, we have precedent for believing the the Scriptures can mean more than their human authors originally intended by the use of the OT by the NT, by the use of the OT by later parts of the OT, and by explicit teaching in 1 Peter 1:10-12)
All of these points actually, I think, allows us to justify the practice of “allegorical” interpretation as it appears in the Fathers (for the most part anyway). That is, if you actually look at the content of the allegories of most of the patristic writers, it is almost universally nothing you could not have learned from a literal interpretation of other scriptures.
And I think that an application of the above criteria can help us to justify that kind of reading, as well as prevent it from becoming completely arbitrary. As God knows everything and is eternal,  and  are already met automatically. But apart from that, one can use all the criteria on a particular passage, taking into account the whole canon.
Further, typological readings often interpret not just other texts, but present experiences according to older texts. I think this is even easier to justify than the previous kinds of readings; in this case, one simply needs to realize that the scriptures, even the narratival portions of the scriptures, were written for our benefit (as scripture constantly asserts, and Paul explicitly), this gives us justification for seeing certain events in the narratives as being a function of deeper principles (historical, moral, soteriological, etc.) which are still in operation today. Thus one can appeal to, for example, God’s judgment on Assyria for its arrogance as justification for interpreting the fall of an empire in one’s own era (if one is living in an era in which that is occuring), since the narrative tells us that God is the kind of God who judges arrogant empires.
Thus, I think there is sufficient justification for readings of scripture other than grammatico-historical readings of the original intention of the human author of a text, which also are not justifications for completely arbitrary readings of texts.