Perhaps the simplest form of chuck spider is three pieces of equal width metal soldered into a form to fit between the chuck jaws. I happened to have a scrap of bronze sheet which I cut into three pieces.
The trick then became how to solder them into the required shape. The stock thickness was such as to just fit into the slots in a 5C collet and this automatically placed them in the correct orientation.
Now we need to solder them without overheating the collet in the process. Fortunately, I have a jeweler's torch with a very small flame so, having fluxed the join, I stood the collet in a pan filled with water up to a level just below the three plates and, working quickly, soldered all three in one pass. When the spider was removed, the collet was only slightly warm to the touch, no warmer than it might become during normal use in the lathe.
If you're uncomfortable using your collets this way, make a jig to hold the stock. Three pieces of metal with a 120 deg included angle shape on the end would work and all three pieces could be gang-milled to the correct profile in one setup
Note that there is one problem with this spider design. If the part it supports requires a central hole, this design is unsuitable since the drill will foul on the spider. There are other spider designs that accommodate central holes. One of mine is pictured in this thread...