matchpoint: Thanks for confirming the dependencies are all there. The purpose behind installing Synaptic was to see if it had more complete descriptions and/or dependency lists than offered through PPM -- not as a replacement for PPM, which seems to work well.
Referring to your thoughtful "Hot off the press" link; I looked at PeppermintOS a few months back and decided it was not for me.
That was a great hint about starting qgis from the terminal. Doing so generates some warning and error messages (file attached to satisfy curiosity). The warnings don't seem to apply to the projections problem. The repeated "ERROR 6: The PNG driver does not support update access to existing datasets" message makes no sense to me. However, this exact message was posted March 12, 2015 on Stack Exchange (https://gis.stackexchange.com/questions ... g-datasets). In three years the post received a couple comments (which also remain opaque to me) but no answer.
The qgis projection problem is proving too recalcitrant, and it is time to let it go. Thanks everybody for your help; your response was more than I anticipated.