How do you politely handle an extremely assertive vendor?

I work for an organization that’s in the process of growing like crazy. Because of this, we often have external vendors (clinic services like ultrasound, chiropractic, specialists) salivating to work with us.

One vendor I’ve been considering working with is extremely assertive, almost to the point where I would prefer not to work with them. I really like their product and think it fits our unique model perfectly, though. The problem is that if the owner/vendor is not immediately responded to, they will follow up via email and cc: all the execs in the company, as well as try to circumvent me to get on exec calendars. Every email sent has read receipts and if I do not acknowledge them, they follow up with a phone call and email with execs cc’d. again.

I am in an upper-management position that oversees all operations and I am responsive to their requests – although it’s not my highest priority. Sometimes it’s a day or two before I respond, which I think is generous given how busy we are.

How can I tell them, nicely, politely and professionally that I am the person who makes the decision about whether or not to add their services, I’m the person that they are going to have the business relationship with and that if we’re going to work together in the future, this behavior needs to stop? I’m trying desperately not to be rude about it but it’s been a challenge finding the right words.