Forgive me for I don't have the book with me and can't remember the Asha'man's name who specializes in traveling.

First off, why is it called a Dreamspike? We know that it prevents the ability to create a gateway in a set distance. And, actually, it's a fairly large distance. Quite a powerful ter'angreal, if you ask me. And, we only ever saw it physically in Tel'aran'rhiod.

So, I propose, in order to work it must be in Tel'aran'rhiod, thus the name "Dreamspike". At first I thought it'd be a weapon to fight Perrin or Egwene or someone in Tel'aran'rhiod, and I bet many others did. The fact that Slayer physically had it THERE instead of in the real world, I think, is proof of this. Plus, and most obviously, it's name. It is the only example we have seen of something in the Dream World reflecting something in the real world, instead of vice-versa.

Now, I know that may be obvious, but I didn't see it stated anywhere else.

Now, the newly introduced Asha'man, with the skill in Portals, but stuck at someplace where the Dreamspike is preventing Portals. How convenient, and obvious, right?

I think it's clear that he is going to find a way around the Dreamspike. That's his purpose in the story is to beat the Dreamspike. Much like how Elayne is going to be one of those "leading the charge" in ter'angreal making, or Nynaeave in healing, and so on.

So, clear set-up for him to defeat the Dreamspike, and likely teach Rand and the others. So...how?

Remember that Perrin couldn't jump THROUGH the Dreamspike shield. However, it could be simply walked through. And once he had it in his possession, he could leap with it. But, the asha'man couldn't Portal within the Dreamspike location--in the real world. We don't know if, inside of Tel'aran'rhiod, they could've. But, as they can still leap within there, and Tel'aran'rhiod is controlled by what you believe is possible...let's say it's a possibility.

My theory is that the Dreamspike will be defeated by this new Asha'man and his talent by creating a Portal TO the World of Dreams. Now, rather this is a weakness in the Dreamspike, or just how he figured out to do it anyways, I'm not sure (more in the next paragraph). He could simply find a way around it, by means of his skill and talent, simply "because". Or, perhaps it needing to be in Tel'aran'rhiod, there is the weakness that a Portal to Tel'aran'rhiod can still be created. I think it's pretty clear it can be turned on and off, as Graendal portaled to where Moridin was and he had it. And then a gateway is needed to take it there. So, I unfortunately do not propose it getting into Tel'aran'rhiod as evidence of this weakness. I simply believe that there is a possibility there, especially combined with his talent, that will allow him to do this, then go into Tel'aran'rhiod and destroy the Dreamspike defending the Black Tower.

Also, I pointed out earlier how it is the only example of something in Tel'aran'rhiod directly affecting the Real World, instead of Vice Versa. Sorry to be vague, but this could also somehow come into play in allowing a Gateway to Tel'aran'rhiod.

Now, as to how he can "simply get around it", let me remind you of other impossibilities that have "simply been gotten around".
1. Channeling in Far Madden gotten around with the use of a ter'angreal.
2. Healing stilling/effects of the Taint
3. Creating a medallion to completely ward off the One Power
4. Etc etc etc.

Just because they didn't think it possible in the AOL doesn't mean it is. Thus, I think the Shadow is going to have a false confidence in it being impenetrable.