Yesterday was exactly six months since I applied, so today I emailed them for an update. Their response contained the following language (highlights are mine):
Please note that processing times vary by applicant, but on average you can expect your application to be processed:
• Global Entry/FAST: up to 5 to 7 months
• NEXUS: 3 to 5 months
• SENTRI: 8 to 10 months
This includes vehicle enrollments. Again, these are average times - your application may take a shorter or longer time to process depending on what the vetting center determines, not when it was submitted. The vetting process cannot be expedited.
Sigh. It's like Charlie Brown trying to kick the football.