AGP 3.0 has no problem reading the content of an sqlite file in, however, adding data from an sqlite file to map hangs at a 'New Query Layer' dialog, where it seems AGP is trying to read the column properties, and fails.
QGIS does not have any problem reading and visualizing the data. Hence, I don not think there is anything wrong with the sqlite file.
Tom - apologies for the delayed response, I was on vacation for the last 2.5 weeks. To your question!
1. I wonder if it has to do with spatial types (geography vs. geometry) for the sqlite database? Reference the following item here.
2. Are there any "custom" settings for the spatial reference? If so, use the Project GP tool to remove the custom settings and try again.