Southern run these: http://www.realtimetrains.co.uk/sea...19/04/01/0000-2359?stp=WVS&show=all&order=wtt
They appear to be one half of route SN3.11 / SN 3.12 from the GTR 2018 timetable consultation.
So perhaps they will continue on to Blackfriars once there is platform capacity freed up at Blackfriars. Combined with the existing Thameslink routes this would provide 4tph in both directions around the loop in the peaks.
I think it's a separate BFR-BFR in the opposite direction around the loop of those southern services we have now (i.e. clockwise am, anticlockwise pm) giving the 4tph in both directions around the loop as you suggest. I think those southern services to/from LBG will stay as they are.