Should a late 2012 Mac Mini be able to drive these two monitors?
Officially, the late 2012 Mac mini will support two monitors in the following combinations:


one HDMI monitor while using one Thunderbolt monitor 
two Thunderbolt monitors. 


As for the supported resolutions, the late 2012 Mac mini supports up to 2560 x 1600 on Thunderbolt monitors or up to 1920 x 1200 on HDMI monitors.

Of course the above is the official position. Your testing has shown you that you can exceed this, but with mixed results.

If you really wanted to get both monitors working you could play around with the resolutions to ensure that they're within the specs I mention above.

You may also find my answer on another question of interest, especially in terms of real life scenarios. In that question the Mac is a MacBook Pro, but the overall findings may interest you.