Click on the banner ad at the top of the home page for the movers who just moved us out of Yung Shue Wan a week ago. Same reason as yours, due to a hefty rent hike, plus we were looking for a more peaceful, greener place, not flooded with visitors and never-ending construction.
Fortunately, Lamma rentals outside the Greater Yung Shue Wan Area are mostly still affordable, despite massive rent increases all over the island, even in the South. We found another place on Lamma, but it's so much less convenient than YSW, of course. Our movers:
http://www.trade-windstransport.com
Highly recommended for these big moves, especially off Lamma to anywhere worldwide, and back! Very experienced in Lamma moves, they moved quite a number from and to Lamma in the last few weeks, including the former tenant of our new flat.
Please let them know how you found them, so they can see that their long-time ad works well.