I couldn't find it quickly in the hoard, but my aunt received a FDC of #1134, the petroleum industry stamp. So, the same time period as yours. It's also an Artcraft or Artmaster cachet cover, addressed to her. At that time she worked for Shell Oil in the typing pool, so there must have been a huge number of them sent out. I believe there was a similar insert or letter with it.
I call these covers commercial usage first-days. Don't have a lot of them, but have started to pick them up when reasonably priced. It's my impression that most of them are #10 envelopes and many collectors don't like them for that reason. The Texas Refinery Company in Ft. Worth did a whole bunch of them in the 1960s.
Here's one from the Omaha telephone company that carried the monthly bill. I'm sure it originally include a first-day cover explanation, but it was not with this cover. The other is from the Texas Refinery Co., with its insert.
Great additions to the thread DonSellos and hy-brasil, thank you for posting. I am sure there are more out there. And Don, the letter advertising the grease and specialty products is a kick to read. Marketing has changed a bit since 1960!