As promised, here is an update:

I set up my 2015 Bianchi Volpe Disc (factory build) with:

1. Shimano SLX HG81 10sp MTB cassette 11-36t.
2. Shimano XT HG95 SIL-TEC 10 Speed Chain.
3. Shimano Deore M592 Shadow 9 Speed MTB Rear Mech.

It shifts well, there are no issues with clearance between rear mech and larger 36t sprocket on the cassette. All gears are usable.

I also added to it a Topeak Super Tourist DX rack for disc brakes. The whole set up cost £97.91 or about $130. The tools I used were a cassette tool, a chain whip, a 4m and 5m allen key, and a small screwdriver.

Here are a two pictures of the final result, for you.

A big thanks to all involved for the help.