Edit: Think I found a matching part: Bourns PTA4543-2010CIB103 - available at Mouser; I'll order 10 and report back. The only downside is the lack of a dust cover, but I may be able to peel away the old cover and glue it to the new potentiometer. Also the lever may need to be modified slightly to mount the knob securely.
Ok, I ordered 10 Bourns PTA4543-2010CIB103 from Mouser and put together a guide of sorts; hope this is legible and help someone save their lovely controller from the landfill. Looks like there's a limit of five attachments per post, so I'll have to use a few posts to cover all images. Again, this is for the Keylab 61 MKII - other controllers may vary. Also, although I've repeated these steps twice without issue, there's a chance that you'll permanently damage your unit - I cannot assume any responsibility for any damage to your equipment or tools.
Before you start, you'll need: a clear work area, containers to hold caps and screws (~4), Philips screwdriver (PH-1 and PH-2), a pair of pliers, possibly a guitar pick, replacement slider(s) and soldering/desoldering tools.
For soldering/desoldering, you can use a gun or iron (at least 30W), leaded solder (60/40 SnPb), soldering flux (preferably no-clean), and your preferred desoldering tool: braid, bulb, or spring-loaded syringe (if you've never desoldered before, you may want to pick up a syringe). There are plenty of resources on the web to help you with desoldering; I'll point out the tricky steps with the slide pots.
For images 1-5:
1: Place the keyboard on a blanket or other protected surface - the tops of the black keys could be scratched if they aren't protected when the keyboard is flipped over. Remove all 9 encoder knobs and 9 slide knobs and place in a container (you'll need one slider knob to test fit later on).
2: Flip the keyboard over and remove all circled screws. Recommend PH-1 for the red-circled screws and PH-2 for blue-circled screws. Recommend using a manual screwdriver for removing and reinstalling all screws throughout this process. Although the screws are easy to identify (the red-circled screws are shorter, have a fine thread and screw into metal, while the blue-circled screws are longer, come to a point and screw into plastic - try not to over-tighten these when reinstalling), it's faster to place the screws into two separate containers with lids that close.
3: The bottom panel is prevented from rattling by thin foam tape at the back of the unit, but it's usually 'stuck' to the metal panel. You can slide a guitar pick just under the metal over and over the foam tape, then slid sideways to "unstick" the tape without damaging the finish.
4: Carefully pull the back down an inch or so; the keybed will remain attached to the back, but there are three connectors to disconnect. The first two are the aftertouch/pressure sensors on the top right-hand side. You may want to apply a dot of black marker to one to avoid mixing them up when reinstalling. The connectors pull out fairly easily with some wiggling - try to avoid pulling the connectors by the wires.
5: There's a far more sensitive flat cable to disconnect towards the middle of the back panel. Slide the keyboard down until just the connector is visible. Then use your fingernail or a plastic tool to pull down on both sides of the slide portion of the connector. These are highlighted in red circles. When they are fully down, the cable should practically fall out. Note that the blue reinforced portion of the cable faces away from you (important for reinstallation).
That's the first 5 out of 17 or so steps; will continue on separate posts...