It appears that TfL aren’t providing any overnight Overground services on New Year’s Eve to Forest Hill and Honor Oak Park.
The final train will be as per a normal Monday evening with the Southern train from London Bridge at 0035, instead the normal Fri/Sat Night Overground service will operate to and from New Cross Gate.
The last connection to Forest Hill by changing at New Cross Gate from Canada Water is at 0031 which meets the Southern train.