Proximity switch wiring

Been having problems with my router. Random limit switch triggering, which seems to be down to either poor connections in a terminal box, or possibly a broken wire. It's all down to the fragile wires from the proximity switches and the difficulty of making reliable connections. Not the first time I've had problems with this particular set of connections; there are a couple of others around the machine where limit switches are daisy-chained and then connect to screened cable to go off through cable chains but they have been completely reliable for years. It is, of course, the most difficult to reach, on the awkward side of the gantry and means climbing on to the machine for access.

The master plan is to rewire the connections in the box - but how? Currently I'm using choc block but it either does not grip the wires or it chews them up. Unfortunately, I don't have any of the fancy versions with clamps rather than bare screws. I have used Wago connectors in various places but they seem a bit aggressive for these fine cables.

Thoughts at the moment are to use crimp-on ferrules, maybe with wire strands folded back over the insulation to give something to crimp to, or solder to better wire tails, with joints reinforced and insulated with heatshrink.

I welcome ideas!