I checked my Call ID this morning and unfortunately it doesn't show up on the analog cordless phones. Not sure if this is a hardware/software limitation, or something to do with the fact that the ht-286 was setup as a gs-100.
Check your ht-286 settings... sometimes you have to tweak the caller-ID scheme, gain, and/or DB level in order to get CID to work properly. There are hundreds of combination's. Try calling your provider and social engineer your way to 3rd/4th level support in order to get the information you need.