Best strategy for removing self-intersections created by the LineBuilder?

Both SDE and SQL Server accept self-intersecting lines, and I have written these before with both Writers.

I suspect Peter your problem is somewhere else.   What errors are you getting in the Output log?

Separately you can use VertexCreator and VertexRemover to Add or Remove Vertices, but I would normally think this is more painful since you would need to first build the vertex index list of all the start vertices that were outside the last hour or data, and figure out which points were the vertices not already in the existing line.  So rebuilding the line in the workspace is fine, and the Writers won’t care how you got the line in the workspace as in the backend they are doing an Insert or Update against the DB with the geometry.

Edit: I will note that if INSERTing new Features to SQL Server to a table hosting ArcGIS services, would generally recommend writing with the SDE Writer in order to trigger related system function and table updates, Eg. generating a new OBJECTID.

I will by default only use SQL Server Writer in this situation for UPDATE DB operations,

Seconding this, writing to SDE via SQL can (and will) cause issues. Reading from SDE via SQL is generally okay.