Similar experience, ended up using a word finder to see what would fit in 14d.
I took the “Alan” in 16a to be an Everyman self-reference.
“At” in 13d seems to be there just for the surface, doesn’t really work for me.
Mprs, indeed, 4000! The current Everyman has made subtle references to milestones in the past - his 100th and 200th puzzles contain allusions to the fact.