Good timing -- I just switched to Trevor and he was throwing up into a trash can at a taco stand next to a mortuary, it's about three blocks south of the impound lot. This is probably the same spot you're talking about.
I noticed three Sultans driving by right away, there are probably more because I have one in my garage but it's still a rare car to see on the road. This may be a hot spot for rare cars in general, because I keep coming back to it and there are regularly Sultans. I think I might need to try different days to get different cars, right now it's Monday in my game but getting close to midnight.
I have indeed switched cars between my characters, I like to get them close and then get out and hide so the first character doesn't run after the "stolen" car. However, you can also shoot around the feet of your character who was driving, and they'll run off.
I also found that passing a car from one character to another can duplicate the vehicle. If you get a car with one person and customize it, then have another character steal it from them, and then put that vehicle in their closed garage, the original character who customized it should be able to retrieve a fully customized copy from the impound lot. Then you'll have two. I found this out accidentally with the Merryweather version of the Canis off-road vehicle. Warning, though, you have to put it in a closed garage, I recommend the 4-car garages. If you park it at Trevor's spots at the strip club, it will just be removed completely and sent to the impound lot. I didn't try the other safehouse garages.
(If you want to test the duplication, I always recommend making sure to empty out your impounded cars first, and I have also noticed impounded cars migrating across save files, turning up in saves that were completely separate or preceded the point where I obtained the car, but this is rare)
And autotheftgrand, I'm also trying Hawick like you said. I spent a few minutes going back and forth from Michael in Hawick to Trevor at the taco stand, but since I'm seeing so many Sultans I will stick with the taco stand area mostly. I also notice two hearses appear at the mortuary when I turn my back, I thought that was only found at the church in Paleto Bay. It's not a car I want but it's cool to see it in LS.