In my view, and it does not matter where we work, sometimes to do what the customer wants we have to “modify” the existing installation. Get the new circuit(s) there. Just make sure that you let them know upfront what you have to do and why you have to do it. Most are happy to patch some drywall if you can explain why you are not causing a fire hazard by cutting a few holes.
My first foreman told me “it can always be done, it's just up to you to figure how it gets done.” And if they say NO to your proposed work, then move on. Don't try to load a 15A circuit over 15A, just as we don't try to load a 200A circuit over 200A. It does not matter the current involved, a fire hazard is a fire hazard. Glad you are rethinking the work, and good luck!