I actually invested money into the now dissolved Canadian company, Nexia Biotechnologies, which was the first to do the spider-goats. You are entirely correctly. Spinning the silk is the harder second part. The gains in reducing cost per meter couldn't keep the pace with similar gains in carbon nanotubes, which competed for many of the same practical applications. Nexia's first path to market was to be superstrong medical sutures. At first, the FDA promised expensive human trials would not be needed since the proteins were naturally occurring. When the FDA later about-faced, it was Game Over for Nexia, who sold the IP rights to a company in Virginia. They also sold the IP behind their proven anti-chemical warfare agents. But the tyrants of the world never used chemical warfare against the US military, so that was (thankfully) also a financial bust.
Nexia was also trying to GMO a plant crop that could grow the silk protein in their leaves. After harvesting, the leaves would be grinded and sifted. However, you're still back to the same Spinning Problem that you highlighted.