I think you could probably get all the information you need from the API but I'm not a user of that right now so can't advise. Links to the relevant version of the APIs are below:
Zephyr Scale API for Server version
Zephyr Scale API for Cloud version
If you're not going down the API route, it's not perfect but as you're already exporting data, if you run the "Test execution results (list)" report for the same criteria and export it, I think you will find the missing data you need. Unfortunately the report export doesn't give the test steps if that's what you're after so you will probably need to do both exports, then join then up on test case ID.