1. Make your claim credible. If you have weak numbers and statistics, but have found something interesting, present it as such.
So what I did was the following, writing a new first paragraph of the paper:
We provide tantalizing evidence that the long-term consequences of dislocation, here due to disaster, may be very different than the literature might suggest. Namely, those who are displaced and move away permanently do better than those who stay. The data are not strong statistically, the comparison group and the convenience sampling is not so rigorous as one might desire, and there is reason to believe the leavers are better educated than the stayers. No one has been able to ask this question before, with data, so in part we are writing to encourage further inquiry. We should note that the literature in city planning suggests that those who were displaced by urban renewal and the disruption of their close knit community, thrive in their new environment of suburban homes. (Herbert Gans, The Urban Villagers and The Levittowners)
Suddenly, the work is in an entirely different context. And rather than some sort of narrative about the data, I suggested a table of the information and a discussion of where the results were manifestly strong, with a proviso about statistical reliability.
That I have provided a new first paragraph for the paper and a new context is just what I do, and some other scholars might do. I had a friend who would write introductions for his students' papers, putting the work in context. I suspect I am quite good at this (I listen for the music, and ignore the details, and so see what is going on), but surely not good enough for my own work!