WooCommerce API – large POST not completing

I’ve written a script for a client that connects to Podio to create a new WooCommerce store item when a certain button is toggled. It’s been working well for items with fewer images of smaller sizes, but it seems to be timing out for many/larger images.

I have adjusted the server PHP settings to well above what should be needed for even the worst-case scenario (max_execution_time=300, post_max_size=128MB, upload_max_filesize=256MB). When initializing the WC client in the script, I’m experimented with providing a timeout argument to override the default 15s value. If I leave the argument as default, I get an error that cURL is timing out. If I increase the timeout value, I am unable to authenticate.

What could I possibly be overlooking here?