Ccould probably minimise the impact by terminating at Kings Cross and for MML services use low level platform A or B*? The other line, if safe to operate with ongoing recovery operations in hand, could be used for short flights of through trains, (say 2xBML and one Sutton loop). It would require enhanced platform staffing to herd passengers onto the correct through trains, but runnning with close headways, that might allow up to two complete three-train flights per hour each way (assuming a transit time of 10 minutes in the core.It's very rare for it to be used for anything other than that I think - I suppose by the time it is considered the issue is usually close to fixed.
Either way these completely avoidable incidents absolutely destroy the service and given some branches are only 2tph it causes major problems for passengers. GTR often don't do an amazing job of diverting in to KGX and it can take a long time to get it set up when they do.
Before anybody jumps on this and says totally impossible, it is only a suggestion within a question aimed at those who might know.
*In normal weekday timetable working, I guess that it would be too difficult to make space on the MML platforms?