How to set up Gnome interface for HiDPI screen?

Your best bet is to keep the 3200x1800 resolution and just change the interface scaling factor of GNOME.

Command line method:

Open a terminal (Ctrl+Alt+T) and execute :

gsettings set org.gnome.desktop.interface scaling-factor 2

You can reset this setting later by running :

gsettings reset org.gnome.desktop.interface scaling-factor

You can use the gnome-tweak-tool:

sudo apt-get install gnome-tweak-tool

Go to "Windows" and set "Window Scaling" to 2:

gnome-tweak-tool screenshot
^{Credit to PCWorld for the screenshot}