I have silver status with BA so it can be advantage...I will ask at BA forum

For our 14 h stepover I was thinking about 3 options
family 2+2 (under 7 kids)
8h transit hotel for my wife and kids and I can hang out in TK lounge or stay in room as well
or
4 times 20USD visa and landsite hotel

if we will decide go via ATH then close hotel to ATH airport and we will be ist at 10-11 am
but its still big planing ....