There are plenty of 2/3" B4 zoom lenses costing well under $10,000 new. And if you get a lens from about 15 years ago before they started branding them as HD, you can get something almost as good as today's HD lenses for a few hundred dollars.
Some people try so hard to get photographic zoom lenses that have some of the same properties as a proper video lens. Why mess around with that? Get a proper video lens, and a proper converter. From experience, I'm telling you, a proper video lens is a much better way to shoot video. You get a lens that's parfocal, has an integrated back-focus adjustment, a constant aperture, and smooth & responsive manual controls. These things make a lens a joy to use, and it translates to better looking video.
Some people try so hard to get photographic zoom lenses that have some of the same properties as a proper video lens. Why mess around with that? Get a proper video lens, and a proper converter. From experience, I'm telling you, a proper video lens is a much better way to shoot video. You get a lens that's parfocal, has an integrated back-focus adjustment, a constant aperture, and smooth & responsive manual controls. These things make a lens a joy to use, and it translates to better looking video.