Alternatives might be the “Pro Max” build described here;
Or, you might be able to get a simple 4 slot m.2 bifurcated carrier card, set the PCIe slot to x8x4x4 and put an m.2-to-10 Gbe adapter in one of the m.2 slots. I’m not 100% sure that bypasses the root cause, but I think it does in that there would be one less device on the PCIe bus (the switch) and all 16 PCIe lanes would be available on the edge connector. Or, more technically 12 of the 16 lanes available through the bifurcation. You still can’t do x4x4x4x4, so you do lose one of the four m.2 slots.