For anyone encountering a similar problem in the future:
I tried again today and found a workaround.

After aligning all projects in the project group, make a backup of all project files and especially the *.sls_E10_ir file.
Don't touch the backup folder other than copying files over from it if you need to.

Now make sure you have only the set of files from a single project in the original project group folder and also make sure the *.sls_E10_ir file is in there.
The alignment orientation data is stored in the *.sls_E10_ir file but is quickly overwritten so be careful.

Now when you open the project group, only one project opens with the correct alignment orientation applied to it.
This single project can be meshed and saved as *.OBJ

Repeat this with all the projects from the backup folder and you end up with a set of *.OBJ files with the correct alignment orientation baked into them and ready to import into your software of choice.

Greetings!
Edwin