Hello Anna,
This is a cool question! I'm not sure if there is a perfect way to do this, but this method came to mind:
What if you did prefix dereplication on the long MinION reads, then used them as the database for open-ref OTU picking? Then all short Illumina reads would get matched to one of the long reads, and any novel diversity would be captured as new OTUs.
In this method, a reference database like greengenes would only be used later on for taxonomy assignment.
This method is not perfect. For example, if a pair of long reads are different in V8 but the same in V1-2, all the Illumina reads from V1-2 could be a 100% match to both of these long reads, and would simply be placed into the read it found first. This is a standing problem whenever comparing reads of different lengths. See this discussion of why global trimming to the same length is good, and local clustering is bad:
I hope this is helpful. You are on the 'cutting edge' out here, so there are no 'conventional' methods yet.
Let us know what you find!
Colin