If your clients aren't interested in the user experience, you'll gain no traction. This is often the case in a large enterprise, where it's not uncommon to hear something along the lines of "We have a deadline to meet so just put the billing screens out there, the data entry clerks will figure them out."
Client resistance to change
If your clients are used to "click here, type the name, tab 3 times, type the phone number, hit space 7 times, type the postal code", any screen changes that might reduce the wasted 'tabbing' or 'spacing', or do an automated lookup by typing the phone number first, are going to disrupt them. Change makes people uncomfortable, especially when the replacement screen trips them up - it makes them feel bad to make mistakes at a job they used to be proficient at.
Burned and burned again
Every executive has been burned by promises that some new IT thing would deliver value. They've spent a fortune on shelfware. They pay for updates that make things worse. They have all experienced upgrade pains in the form of "when I upgraded my iPhone to a new version of iOS, my old iPhone was too slow and needed to be replaced to run all those fancy graphics." Whether or not they were your fault is immaterial - they just downloaded a new version of Windows 8 and know that change doesn't mean better. Making empty promises that "a UX culture will make our stuff better" will ring hollow in their ears.
If the stakeholders are not clamoring for change, top management will have no incentive to embrace the UX culture. So that suggests one possible place to start.
Bring in the stakeholders to your experiment, but don't emphasize it's a UX effort. Call it a "time and motion study". Invite the supervisor of the billing area to participate in a usability lab to test new billing application screens. Show how quickly a new hire picks up the system with the improved screens. Show how much more productive a worker can be if they convert to the new system. Compare to a new hire testing the old screens, and an experienced data entry clerk entering data in the old screens. If the stakeholders run the stopwatches themselves, and if they can see actual productivity gains from the new UI, their next question will be "how fast can you deliver this?" That's your light turning from red to green.
Once your stakeholders and executives realize actual value from investing in a well designed UX, that's the time to introduce the roadmap to creating a UX culture. Show them how other areas of the company can benefit from usability studies. Meet with other teams, see if you can sell them on the value by helping them run through a UX lab. Once you make UX a desirable attribute for every product, you'll know you have created a UX culture.