Finding data to validate results
The snarky answer is that it's better to find a matching dataset at the experimental design phase (i.e. before these studies are carried out), so that the bioinformatics component on the other side of things ends up being a lot easier and more robust. Although it can be quite time consuming to do a database search at the start, it's even harder to find matching projects if the legwork hasn't been done during the design phase. Researchers should be thinking about how hypotheses will be validated before the experiments are carried out.

Every additional characteristic that is chosen for comparison adds complications with regards to matching data, and reduces the applicability of results when there is a mismatch. You would have to be somewhat lucky to be able to find a IBD-Crohn's dataset with paired RNA-seq data and 16s-seq (presumably short-read; is 454 good enough?) from a specific non-stool tissue.

Apart from the places you've already looked, there's dbGaP and SRA. Given the number of characteristics that have been mentioned, I expect you'll have to make some compromises when comparing other datasets.