Can I restrict Nexus 7 2013 LTE to 2G/3G, instead of just 2G? In the settings on Google Nexus 7 2013 LTE, there is an option to restrict the device to 2G networks for better battery life, which makes it use 2.75G GSM EDGE.

Why is there no option to do the same for 3G?  Isn't 3G UMTS/HSPA+ also better in the battery-life department than 4G LTE?  Is there any app to address the limitation?
What version of Android you currently have on your Nexus device?

I have (I think) exactly the same device, as you (ASUS Nexus 7 II (2013) LTE) and three days ago it was upgradred from 4.3.0 to 4.4.2 KitKat (I issued manual upgrade, by connecting to WiFi network and going to Settings &gt; About phone &gt; System Updates).

After upgrade, option you're referring to (Settings &gt; Wireless &amp; networks &gt; More &gt; Mobile Networks &gt;  Use only 2G networks) has been changed to Preferred network with options: 4G, 3G and 2G.

Now you can fully control, which kind of network your tablet access and you can limit it to use only 3G networks (second option), which has full fallback to 2G network, if 3G one isn't accessible in your area.