Answer: First of all, your cats must be quite happy with their sunroom! I haven't tried to grow outdoor vines inside, but passion vine (Passiflora) is recommended as a greenhouse plant or a houseplant for cold climates. They can grow 20-30 feet tall, and climb by tendrils, so they'd need something to grab onto. There are many different varieties and some are evergreen, semi-evergreen, or deciduous, so you'd probably want to choose an evergreen. They have very showy flowers, available in many colors. P. jamesonii is evergreen with salmon to coral flowers; P. Lavender Lady is also evergreen; P. vitifolia has red flowers.
Star jasmine is another vining plant to consider. It's evergreen, has very fragrant flowers, and grows to 20 feet.
Before training to your wall, I suggest experimenting with how they do in a large container with a trellis in it. Good luck!
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