I’ve been working for the past several years with student independent research projects using DNA barcoding (and metagenomic barcoding). The end product of these projects is generally a poster presentation focusing on the barcoding (although this semester, I taught a seminar that specifically incorporated iNat and led to posters analyzing iNat (bioblitz) data). I’m thinking of ways to more organically combine the two sets of data. One thought – if resources for eDNA sampling become available – would be for them to compare species diversity between the two data sets. If they are doing a standard barcoding project focusing on one taxonomic group via Sanger sequencing, I’m not sure how to meaningfully incorporate iNat in the research (as opposed to interesting background information). I’d be interested in hearing if others have made this connection and how they did so.
I haven’t done any iNat/sequencing projects with students myself, but for the single group/Sanger sequencing projects, I think you could do a lot by focusing on groups and/or life stages that are poorly documented, especially with publicly available images. I’m going to give Lepidoptera examples because that’s my particular jam, but these could apply to other taxa (other insects, blooming vs. non-blooming plants, etc.). There are a lot of Lepidoptera that are well-documented (on iNat and elsewhere) but have no/very few records for the caterpillars. In some cases this is because caterpillars of closely related species can’t (as far as we know) be physically distinguished, but a lot of times it’s because we just don’t know which caterpillar turns into which adult.
You could do either sample-first approaches (collect specimens, document them on iNat, and ID them with DNA barcoding) or iNat-first approaches (look for species that are locally well-documented as adults but poorly documented as immatures and see if you can fill that gap).
Another option might be if you’re “lucky” enough to have two or more morphologically similar species in your area, your students could collect a bunch, identify them morphologically, and then use DNA barcoding to see how accurate their IDs are. If there’s a lot of overlap, that could be shared with the iNat community to encourage people to be very careful of species-level IDs in that group
I’m sorry I missed seeing this post until now. If you’re looking for DNA barcoding, let me encourage you to take a look at https://dnabarcoding101.org/
CSHL has both student and citizen science DNA barcoding initiatives (including with partner sites in other states) and grant money for barcoding ants, mosquitoes, and beetles, and offers educator training as well (see https://dnalc.cshl.edu/programs/teacher_training.html).
And when that doesn’t work? 
https://www.inaturalist.org/observations/69462345
By the way, be sure to check out our target species of beetles: https://dnabarcoding101.org/citizen/cdbn/map.html