In the UK, the distributor up until about 2 years ago still has all the kit to service CLM feeders. Presumably some of the other regional distributors do too although I believe some rely and returning them to Essemtec.
Taking the (thin) side off to clear out a jam is simple enough, although it shouldn't be required often. You can also carefully remove the front plate to get at the lanes from that angle too. I haven't personally dared attempt to meddle with the sprocket assembly, it looks very complex and my service engineer tell me they do indeed have a jig back at base as well as a proper test bench with comms etc.
As @zjr says, make sure the nylon ring in the spool holder runs freely, also make sure the metal/magnetic surfaces of the two halves of the spool holder are not touching and rubbing each other. When that happens you get a nasty black soot that then completely ruins the surface as its very abrasive. As the feeders have aged I have taken to doubling up in the teflon sheets in the spool assembly to maintain the gap and keep them running nicely (I'm guessing they are slowly spreading out given they appear to be made from FR4). If they stop running freely a tight/stiff spool, can pull the tape forwards when the spool motor runs for other lanes.