It would be great if you could identify something about the document that causes this issue -- a 38MB document is pretty large, so this might have something to do with it. Can you try with a super small oam file with just a single rectangle and see if the file size is related? Larger file sizes require a bit more time to process (unzipping, moving files, uploading).
A pretty common issue when uploading OAM files with this plugin and getting them to appear is complications with flexible documents. There's a big section devoted to this in the Wordpress Plugin thread: Tumult Hype Animations Wordpress Plugin. The takeaway is that you need to make other changes to your Hype document if you are setting 100% height for your first scene. In 99% of cases unchecking the 'height' checkbox fixes display issues for folks.
Once you get a OAM uploaded, do you find that it sometimes loads and sometimes doesn't on the page? Or does the shortcode just unpredictably fail during upload?