Rebuilding a 20 spoke 404 firecrest - spoke choice for maximal stiffness

Is the wheel deflecting or the hub/frame connection? Maybe try a steel QR (a trainer QR for example). Are the spokes tensioned well? (Try a phone app to see if they are somewhat close if you don’t have a tension gauge), Are you using the thinner pads for thicker rims or normal pads?

Using what you have, Powertap 20h and Zipp 404. How are they laced? Maybe you can lace them with all the spoke heads toward the interior, giving you a slightly larger bracing angle.

I’d get some thick spokes. I don’t think rounder will help, but just more material. You’ll need to ream out the spoke holes a bit with a dremel and a diamond ream. I’d try Pillar 1432 aero spokes, which you can find for a reasonable price from CSC on ebay relative to Sapim/DT Swiss.
If the nipples are external, you can try making them internal. I don’t think anyone makes an internal nipple for a normal sized hole though, maybe try a washer. This should net a bit more bracing angle.

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