The Append tool needs to be run as the table owner from what I understand. This is because by default it recreates the spatial index. I found you can get around this by ticking the "Maintain Spatial Index" setting in Environment Settings (under Geodatabase Advanced in 10.2.2).
Geoprocessor gp = new Geoprocessor();
You can then run the tool using OSA or any other authorised user that is not the table owner, and you don't need an exclusive lock.