6oz is nothing.
My original recipe for Ginger Ale uses 40oz, but I add it to the boil, which "cooks" much of the harsh/bitter flavor out of it. My current, Ginger Honey Wheat, only uses 2.5oz in the secondary, but is a little bitter.
I think the next time I make it, I'll omit the late hop addition.
As for your batch, age it awhile.
Some of the bitterness will age out.
The next time you make yours, cut back the 60 min hops to 1oz, that will cut back on some some of the bittering.
