How to reliably secure stranded wire in terminal block?
(This is info already mentioned in the comments on the question — but nobody wrote an actual answer, so I'm doing that. It does also agree with my small experience.)

Do not use any solder at all. Use a wire ferrule, which is a metal sleeve that slides over the (straight) strands and is crimped in place, making a solid end that can be clamped securely by a screw terminal of the type you are using.

Caveats:


Use the proper crimp tool, which will leave a textured surface that is readily gripped by the terminal and resists sliding out more.
Adding the ferrule will increase the size of the wire end, possibly too large to fit in the screw terminal. (This should not be a problem if one of the options you have considered is doubling over the wire.)




This picture shows several sizes of ferrules, two ferrules crimped on 22-gauge stranded wire, and the crimp tool I used ($21 when I bought it).

The plastic part of the ferrule guides the strands in, covers any exposed metal, provides some strain relief, and identifies the size of the ferrule. Caution: ferrule makers do not all use the same color scheme!