So my strategy, in theory, should be working?
Yes.
One other possibility to check is that you could have a bad connection in your pre-fab daisy-chain -- it's rare, but it has happened before.
You can narrow that down using the "divide and conquer" troubleshooting technique.
If the ground connection at the microswitch is point A and the farthest-away connector in the daisy-chain is point Z, check for continuity from A to Z.
If you don't have continuity, check from A to L.
- If it is good, the problem is somewhere between L and Z.
- If it is bad, the problem is somewhere between A and L.
Keep dividing the circuit in half until you narrow down exactly where the problem is.

Scott