How to "harden" sugar caramel?

I'll take a shot at answering, but unfortunately I don't think you can just harden your caramel directly. The candy stages are what they are, as I'm sure you're aware. The soft crack stage, between 270-290 F is where your sugar will become solid, but still be a bit pliable. It will bend slightly before it breaks. Depending on the exact shape your making, and how much weight it will be supporting, how long you need it to last, etc, you may consider only cooking your sugar to soft crack, instead of to the hard crack or caramel stage.

Past 290F, you're approaching hard crack. The sugar will be even harder than before, but will become more brittle. You know that toffee is cooked to 300 F. As you get past 300 F and actually caramelize the sugar it will become increasingly brittle.

If you want less fragility, but still want the color and flavor of caramelized sugar, you could caramelize the sugar initially, add water (carefully. Use a big pan and make sure you stand back) then cook again until it's only at soft crack or the earlier stages of hard crack.

I tried looking into different sugar substitutes to see if they have different properties when melted and re crystallized, but unfortunately I couldn't find anything. I've seen isomalt used to make edible hair, but I haven't worked with it personally, so I can't say if that's an avenue worth exploring.

The only other option I can really think of is to change the material. Does it have to be pure caramel? Could you use chocolate or make some kind of nut flour based candy? Or even using toffee instead of pure caramel? I acknowledge those suggestions are basically ways to make an inherently thicker substance, which would not set clear, or allow for fine details or delicate strands of sugar magic.

Lace cookies (basically toffee with nut flour) come to mind as being thin and pretty/delicate, but having enough strength to make a small cookie sandwich with.

Hopefully, this is some help.

The hotter you cook sugar, the more brittle the end product. Referring to the stages of cooked sugar, we see that only from "hard crack" stage onwards (146+ °C) the sugar turns brittle.

That said, many recipes for croquembouche do call for the sugar to be cooked to caramel stage at 160 °C. The caramel in these recipes is thus expected to be brittle. You will find that croquembouche recipes often tell you to dunk your pan in cold water as soon as you reach the desired temperature, to avoid overcooking the sugar.

If you are making something other than a croquembouche, you can try cooking the sugar to a lower temperature (which means you will have to forego the color and flavor of caramel). You could also experiment with adding small amounts of butter and/or cream to the caramel, effectively making a much thicker variant of caramel sauce.