I don't think Sling will be able to help you on this.
The reason you can see it remotely on a PC but not on an iPhone is that Slingplayer on a PC does not need full port forwarding and can actually work around it. The iPhone app, along with other Mobile apps, SlingCatcher and older Classic Slingboxes MUST have full port forwarding enabled to work remotely.
Now, like you I have done all the research into setting up port forwarding on the BTHomeHub and I am convinced I have followed the instructions and done everything correctly. But I still cannot access my Classic Slingbox or use my remote SlingCatcher, although I can see my Pro-HD on my laptop.
BT are notorious for all the tweaking they do outside of normal practice and I am reasonably convinced they are doing something inside the Home Hub that prevents the port forwarding from working correctly (I cannot access my NAS remotely either). So I think their support line should be your next port of call. I hope you have more success than I did.
But if you do ever find the solution I will be grateful if you post it here.