Have you evaluated the dual-fisheye plug-in by Ichi Hirota? The plug-in is free. There are some inexpensive add-ons that can speed up the workflow.
This is a series of apps that includes DNG transfer to mobile and Stitching and mobile. If you have questions, ask them here.
For HDR pictures inside the THETA Z1, there are two modes:
If you are using a tripod, HDR is best. If you are holding the camera on a selfie stick Hh HDR is best.
Can you post the stitching problem? (screenshot of small area)
If you want to post the actual image, you’ll need to put the image up on someplace like Google Drive and then put a link to the image on this forum.
Perhaps unrelated to HDR internal rendering, I was thinking of doing tests with the stitching for bracketed shots.
I do not know if the settings below have any impact on the internal HDR. I do not think the settings below can be adjusted with the official mobile app, but @jcasman and I looking into building a mobile app to make these adjustments. I’ve been waiting because I’m not sure what “dynamic” stitching is what problems are solved with “static” versus “dynamic” stitching.