How do you solve PLA corner-curling short of printing really, REALLY slow?
Cura has an additional setting that you can make visible called "Lift Head". My recommendation is that you do the following:


Set your minimum print speed to something actually reasonable like 30mm/s or higher. Printing too slowly negates the following two settings and is not beneficial to printing small features.
Set your minimum layer time to something higher, like 15s or so. The slower you print, the higher this number needs to be. Using too small of a minimum print time prevents adequate layer cooling.
Enable "Lift Head". This must be used to allow the small features on your print to properly cool. Without the "Lift Head" setting, your nozzle will remain parked on your print and provide both radiant and convective heat which prevents cooling and causes sagging of small features.


The combination of these settings will rapidly deposit the layer, then move the nozzle high and away from the print until the minimum layer time is reached, such that the radiant heat from the nozzle doesn't continue to heat the soft PLA while it's trying to cool. 

Enabling all three is how I got perfect tiny features on all of the printers here at my office - a fleabay i3 clone, an Anet A8, and a couple Monoprice printers of various levels. 

Edit:

I forgot to mention, keep your bed temperature at a reasonable setting too. For PLA, normally people may recommend up to 70C, but realistically, for very small prints, you can keep your bed much colder without detrimental effects. For tiny items, my PLA prints used to use a bed temperature of about 30-40 C depending on the specific filament. Very tiny prints are unlikely to warp even with a cold bed.

Basically, the colder the bed is, the less heat is getting conducted up through the print to the top layers that are molten, and the faster those layers cool. Keep the bed temp down and it'll benefit your layer cooling.