Some Huawei data sticks carry phone-capability according to their "Mobile Partner" software (there's support for it in the disabled modules. Mobile Partner is a pile of shit but sometimes it's actually useful).

I do not know however which exact sticks can do this.

3G module with bonus GPS: http://www.ebay.com/itm/261346638302

Appears to be a Qualcomm QSC6270-based module.

Could one solder this 3G module on the board from the article?

http://www.micro4you.com/store/sim900-gprs/gsm-module.html (just removing the GPRS module and soldering the 3G?)

Not possible, SIM900 has 68 pins and SIM5320 has 80.

That listing is blocked in France due to "legal restrictions". Is it a module designed for laptops, or something more general?

It's this: http://wm.sim.com/producten.aspx?id=1029

There are lots of them. Just look at what GTA04 and Neo900 are using (Option and Cinterion). Such project can't accept closed baseband being highly integrated with main CPU and RAM like most of modern smartphones do, so they use ready 3G/LTE modules to move it out as a USB peripheral in CPU perspective.

Sierra Wireless have 3G modules, although they're not particularly simple or cheap.