The best commercial load data I have seen for the .404 comes from Hornadys' latest loading manual. They claim that Reloder 17 was the best powder in their test rifle (a CZ 550) with their bullets.

Their maximum load with Reloder 17 and their 400 grain bullets was 84.0 grains for 2350 out of a 24 inch barrel. Their maximum loads from the various 4350's are as follows:
H-4350 78.9 grains for 2200 fps
Accurate 4350 80.9 grains for 2250 fps
IMR 4350 83.6 grains for 2250 fps

Powders that are similar in burn rate to Reloder 17 would include Vihta Vouri N 550, Norma URP, and Hodgdon powders' Hybrid 100. Their are of course others that are near by in burn rate. Try Vihta Vouri's and Norma's websites for loading data.

Chronograph your loads. If they exceed 2200-2300 fps by much back down. The .404 is a wonderful cartridge, but it is not a .416 Weatherby.