Source an internal/hub derailleur for Bianchi Bergamo Is this really such a novel piece of equipment?

2006 Bianchi Bergamo internal/hub derailleur

I commute with a lot of weight on the rack and pop spokes in my rear wheel at least a couple of times a year. I had it rebuilt and had a good six-month run until last week. I asked a local shop to spec a full replacement wheel so I'd have a spare that I could just drop in (so I can then get the other wheel fixed up when convenient, without losing the use of the bike in the meantime).

They came back saying that the hub alone would be $350 USD. The whole bike was something like $600 USD.

I can't find a source for this, and now I'm concerned that someday that thing is going to break and then where will I be? Any suggested courses of action?
You could order your own replacement hub, for example Universal currently lists the 36h Dual Drive (Disc) for $187.  These hubs are a relative rarity, and I don't doubt that your LBS price would be above $300.  Bianchi presumably got them in bulk for a bargain when they specified this frame.

If you're carrying heavy loads upgrading to 36h is certainly a reasonable solution and will definitely help.  You can also select a beefier rim - I personally like the Salsa Delgado, but rims such as the Velocity Dyad and Sun Rhyno Lite are perfectly fine as well. Lastly, get a professional wheel build.  All told you're probably looking at at least $320, most of which is dominated by the price of your hub.

Depending on your riding conditions and preferences, another solution might be to replace your Dual Drive hub with a normal 9-speed derailleur hub. This will cost a bit more than usual in the near term (you'll need to replace the shifter and the derailleur), but you'll have more wheels at your disposal.  Craigslist and eBay can be a treasure trove of relatively inexpensive handbuilt wheelsets, if you're patient.