One year update: it turns out my solution does not quite work.
Although the TPE-521ES will boot up both devices in the Class 2 profile (7 Watts each), it turns out the AP One Mini will occasionally use a tad bit more than 7W in operation. For example, when doing a big download over WiFi (multi gigabytes) the AP One Mini would try to use more than 7 watts, and the PoE switch would cut the power, causing the AP to reboot.
Although the TPE-P521ES has settings to allow custom per-device milliWatt limits, I was never able to find settings that would allow both devices to boot up and remain running under load.
The switch allows you to have Two class 2 devices (7W each = 14W total power budget) but if you try to do a custom split (8W + 6W = 14W, or 9W + 5W = 14W) it never allows more than one device at a time to be powered on. Seems like a bug in the TrendNet.