How to Install Gutters Under This Roof
Your situation is not that uncommon.

For the hangers, you may use roof mounted brackets / hangers or you may add blocking behind them as the other answer suggested.

You can also have a custom made gutter that has an angled flange that sticks under the shingles and sits on the roof, or just have a deeper gutter that sits against that fascia.

As suggested by @riseagainst using the columns or rain chains is your best bet.