Matt, depending on what all is going on in the client’s custom Lightning page, I think that the inverse would be the recommended approach — you can modify your Lightning Experience page to include a Skuid Page (using the Skuid Page Lightning Component) as well as whatever other Lightning Components that your client has made.

Hi Zach, 

I was hoping there was a different solution but I also understand it is a tough request. 
Given my use case here I don’t think your solution will work for what we are trying to achieve.

My thanks however for giving this some thought =)