Polycom is usually 24VDC, non-standard (i.e. not 802.3af) PoE, on unused pairs.

You can't use a standard PoE injector with those. Even if they come up, they won't link because the data pairs are not isolated enough. (IEEE standard PoE runs the power on the same pairs with data, and capacitively couples the data through to the device.)

Any device that is truly 10/100/1000 should have no problem selecting 10/100 when talking to your PoE injectors. The weak part of auto negotiation is the duplex selection, NOT speed (clock speed is easy to detect.)