alu gutters?
do those have to be custom made?
have only seen your normal galvanized and PVC in the stores
@SAguy why not try some more contractors for your list and tie that 'carport' into your existing roof?
1 out of a few options would be to maybe:
build the roof over your existing roof and then sloping it towards gate (assuming your jojo is there where that gutter is out-letting to).
you can do a full lip channel frame and then on that low end add it's own gutter.
just please whatever you do, don't put the lip'd end on the 'outside' where the gutter will be.
as for not having it be "hokkie"-like, only thing would be to add like ornamental bracings for some aesthetics
besides a "carport" being pretty much that kind of structure, your placement also doesn't quite allow for much options in terms of looks.
can always try add some wood after you have done the main structure.