How can I copy a kit from one account to another?

I recreate client brandings and implement them on our own servers.

Many clients have typekit for their websites, and instead of going through the hassle of them adding our domain to their kit, we just recreate the kit.

Is there a way to take the typekit kit JS file (ie: https://use.typekit.net/hzv2aqa.js) or ID and export it to our own typekit account, or is there a way for me to access a kit via the API i don't have access to, just to "copy it" to my account?

I'm assuming not, but can't hurt to ask.

What I'm going to try to do if the above isn't possible is write a script to download the js file, pull out the fonts within it, and then create the kit in my account through the API.