I was in the exact situation as the OP. We are also going to expand our lanai, so I didn't want a big investment, but we put a hot tub in and I wanted some privacy. Lowe's will not cut the blinds for you, nor will HD. You could maybe find a 3 ft and a 4 ft, if you don't mind the "look" being a bit off. That's what we did with the plastic mini-blinds from Walmart. They are very cheap, and they will work for a while until we expand and I do something custom.
I also considered doing rods and curtains, as mentioned. I love the look, but I tried it on one side, and the breeze was a bit much, or if we had the ceiling fan on, they billowed out. You can tie them back to avoid that, but then when you untie to have the privacy....we didn't have a solution for that.