The new SIM card from Verizon works! I first did some testing using XCTU, and I can set the Carrier Profile (CP) either to 3-Verizon, or to 0-Auto-detect, and it registers and works successfully. (Not surprisingly, it never registers when CP is set to 2 (AT&T), and I also presume that setting CP=0 in an AT&T-only coverage area would not work).
Back on the Mayfly, I changed the APN value to ‘vzwinternet’, and it works there too. (The APN value of ‘-‘ will also work; this is the default setting in XCTU.)