*very* unbalanced group sizes for DE
Random partitioning (as you have done) seems like a reasonable thing to do to work out what's going on. From the results you have suggested, it looks like DESeq2 is performing better than EdgeR, so use DESeq2. Can you show the volcano plots and the partition sizes?

Note: I'm a little bit biased in this, because DESeq2 is what I prefer to use (particularly where Salmon is not appropriate).