JFK2LA
If a move is best for you, i can highly recommend from experience a number of places along the M11 corridor.
Theydon Bois
Ongar
Epping
Bishops Stortford
Great Dunmow
GD is furthest, but for a 6am start the drive is 35-40 mins, and 1hr in traffic - East Herts, and West Essex still have some really nice towns and villages in very commutable times to LCY, plus the presence of STN means there are a number of companies tailored towards crew searching for somewhere to live.
If renting is the short term solution better deals are in towns/villages without a mainline/underground stn, head for Chipping Ongar, Gt Dunmow and surrounding little villages.