Better to use the cultivar "Emerald Green'/'Smaragd'/'Emerald Beauty' (different names for the same cultivar), since it is much smaller - 15-18' x 3-6', and so will be a LOT easier to keep to 6'. 'GG' will grow to 40-60' and half that wide, so you would be REALLY fighting its natural tendencies. If you want a narrow hedge, 2-3', then look for the cultivar 'De Groot's Spire', since it stays under 15' and is no more than 3-4' wide.

'Green Giant' is fragrant and is supposed to be deer resistant, though I've not tested here among our large deer herd to say for sure. They are very fast growers...faster than the other thuja.

It is my understanding that most of the other thuja are good deer food, so I don't have any outside my fence. I have 3 in pots on a deck and 2 inside my fence.

Osmanthus fragrans is an evergreen, very fragrant shrub. It's not a particularly fast grower and it could take a few years to fill out. However, it can take just about any shaping you want to do to it. Deer don't touch ours. Just another option.

Cameron