That's brilliant. My only suggestion: change "just a few minutes" to a bigger number, like ""five minutes or so." That should work even better!
When I was working my exit I avoided FS as much as I could, but like you I had to go a few times. To avoid blowing my cover I came up with similar strategies (but yours is even better).
For example, we had a CO who suggested we go to the door with nothing in hand but a bible and ask if we could share a scripture. So I used that approach. At the door almost no one wanted me to read a scripture to them, although a few people did. In that case, I read it to them and said, "Next time we are in the neighborhood, I will bring you a magazine that discusses this wonderful promise from the bible." End of presentation, bye-bye.
It appeared to the fellow dub working with me that I was a mature dub with a novel approach designed to get lots of RVs. Of course, I never went back on any return visits.
[It's been several years so I can't remember chapter and verse; it was the scripture that says heaven and earth may pass away but the earth lasts forever].