I think the AW will probably too off road for what I want.
Here is something I've learned the hardway with offroading a big bike like the boxer GS you can never have a too offroad orientated tyre especially if your a novice riding lanes you dont know.
Lanes have a habit of getting much harder really quick and you can find yourself committed where you can't go back your only option is forward it getting worse before it gets better.
Having something like an AW will ensure you have a good level of grip to deal with most things that you'll come across, there is nothing worse that finding yourself in deep shit and not having the grip to get out it.
An aggressive tyre will give you the confidence and help you relax which is so important, everyone says you shouldn't ride alone offroad which is correct but people do anyway so its doubly important in my view, that you have a very grippy tyre, you stuffed if your alone and you've no traction. I'm not saying the AW is any better or worse than the E07...I wondered whether to get one but don't overthink it. Get your confidence and ability then look at different tyre options once you understand better what your buying and what the lanes are like that you'll ride.
Besides the fun you can have offroad from the better tyres by far outweighs the loss of balls out riding on tarmac.
I was out on Sunday in Yorkshire and the pace was "brisk" but not balls out and I had no worries about the tyres, I find them fine in the wet, so I don't see them as a compromise day to day on road because I don't try and ride the GS like you would a more road focused bike that's only fun to ride fast.
I still class myself as a relatively inexperienced offroad rider so I depend on the tyres for grip because I dont have the skills to get away with a more road orientated tyre and the GS is one heavy bike to lift alone so the less you drop it the better.
Whether you buy the E07 or AW just make a choice and try it....Next time I'm out I''ll give you a shout if you like but up to the may bank holiday is out due to other commitments apart from some short rides.