It's pretty unusual for greyhounds to be 'snappy' at all, let alone to become snappy without there being a reason for it (actually it's very unusual for ANY dog to snap without there being a reason, a build-up or trigger). As others have said: vet check.
Without seeing the behaviour happening though it's hard - and possibly unsafe - to say. Hopefully the behaviourist will visit you and see what's going on. If this isn't suggested I'd be very surprised.
When and in what circumstances, exactly, is he growling and what do you do then?
When is he stealing food? Off your plates, or from kitchen counters or tables when nobody's around?
What and how much do you feed him? How much exercise do you give him? Does he have a chance to play and run free? Does he have a place he can feel 'safe' in your house, where he can sleep and relax without being disturbed?
All these things could affect his behaviour but in most cases simple changes can be made to help the situation, assuming you're willing to try.
Some dogs are fine being left alone (though periods of more than four hours in one go aren't good), so your increase in hours may not be a problem for your dog.
Note also that some rescue organisations won't or can't rehome dogs which have bitten, depending on the circumstances, so if you are talking a proper bite and not a warning air-snap, you could be sealing the dog's fate already; it may also affect any insurance policy you hold for him. Which is why it's important that you have a visit from a qualified behaviourist and preferably one attached to the rescue you got him from.