We've found the problem. For the edification of anyone else who may encounter this, here's the explanation. Starting with this:
"Option 60 is included in the initial DHCP discover message that a DHCP client broadcasts in search of an IP address. Option 60 is used by DHCP clients (LAPs in this case) in order to identify itself to the DHCP server.
If the access point is ordered with the Service Provider option (AIR-OPT60-DHCP selected), the VCI string for that access point is different than those listed above. The VCI string includes the ServiceProvider option. For example, a 1260 with this option returns this VCI string: Cisco AP c1260-ServiceProvider.
If the Cisco AP runs 18.104.22.168 or above (12.4 (23c) JA2 or above) and if a bootloader environmental variable (env_vars) namedDHCP_OPTION_60 exists in flash, the value is appended to the VCI. If you order a Cisco AP with the Service Provider option, it will (by default) include the -ServiceProvider suffix; however, you can include other values into DHCP_OPTION_60 as well."
Whoever ordered these APs apparently selected the Service Provider option, so the "Cisco AP c3500" VCI string wasn't adequate. We created a new VCI with "-ServiceProvider" appended, and that did the trick.