A lot of things here don't make sense. A ticket that is refunded can't be changed or have seats assigned (as you pointed out). Since you have all the nonsense in writing you are in pretty good shape IMHO. Since LH is unwilling to address this issue, you are likely best served by reaching out to the SOEP for resolution.
Now, I have to say, with multiple changes initiated by you including adding stopovers in FRA etc. ... things can go wrong. That said, if you have all the documentation and ticket exchange Emails from LH, it is LH's problem and not yours. Did you by any chance ignore Emails from LH to 'contact us' wrt changes? LH is known to cancel tickets that require re-issuing when customers don't respond (bad practice) .
If you complain to the SOEP, keep it simple, much simpler than what you have here. You changed the ticket, you have the new ticket receipt and LH charged your CC ... LH refused transportation. That honestly is all that matters. Also a statement that no refund and no communication has been received.