This is an awesome question and it just so happens I had this exact same issue come up at our agency when I first introduced Unbounce. I had to convince both our designers AND development teams that Unbounce as a viable platform for our agency.
Believe it or not convincing my creative director and design team was pretty easy. For development it was a little harder. As the marketer in the bunch I had to unite the two teams because I felt strongly about adding this tool to my toolkit.
The reason I felt strongly that I needed an Unbounce solution was simple. I believed @Oli_Gardner when he says NSAMCWADLP. I had tons of PPC traffic going to evergreen landing pages that I had no control over the look/feel or content.
What I did to convince our design team was I took a PSD that they had created for a landing page and built it in unbounce matching pixel for pixel. Including the use of a custom font. When they say that it was possible to make the live pages look like their designs, they were happy. Note: since that time we have really focused in on the principles of conversion centered design, and unbounce platform specific things that can/can’t be done with ease.
My dev team took a little longer to convince. They were afraid that I was trying to create new workflows outside of our normal process because something was “broken”. This could not have been further from the truth. Remember that PSD that I turned into an Unbouce page for design? Well it took one of our devs 8h to turn that into a page on the client’s site. It took me less than 4. It was the FIRST time I had used the platform. Since then I have gotten MUCH faster
I was able to prove to dev that for these dedicated marketing campaigns that using a hosted platform solution was far more efficient. Sometimes I need a page to be live for just a day or two. Sometimes they run for months and end up with 10-15 iterations through a/b testing… either way with marketing building/testing them we are able to deliver results faster for our clients than having to pull a dev off a major web build to spin up a quick landing page for a new PPC campaign.
Once our account managers saw how we were using the platform they were able to start to sell it as part of our marketing engagements and increasing our retainers… needless to say with a little “show and tell” I was able to get company buy-in in just a couple of weeks.
To your point, it is not easy to convince others to try something new. But if you believe that you can drive better results with a new tool you will be successful!