I'm not really the one to ask. I'd get in touch with Tim Lively (I know I keep recommending him, but I swear I'm not putting him above other smiths--he's just very good about answering questions.)
There are ways to "recarbonize" steel, but I wouldn't trust myself to do it. Better to talk to an expert.
What you can do with almost any steel is make two flat blanks of the steel and one of the carbon steel you prefer for its cutting ability. You can weld (if you are able to forge weld) the three pieces together with the cutting surface in the middle. Then when the blade is shaped and ground, the outsides will have the strength of those damascus barrels but the center will hold an edge. Another way is to make a U-channel out of one blank for the "outside" and weld the center bit into it. This is VERY difficult, at least for me. It's enough challenge for me to get two correct flat welds without removing all carbon from the steel. Forge welding is tricky that way. You almost have to heat to the point of some decarb, because it's the clear sign that you've reached welding temperature. But every second you keep it sparking like that, you're losing carbon from the finished steel. It's a balancing act.
However, carbon steel heated to yellow heat and shooting sparks in all directions is one of the coolest things I've ever seen. I'm not sure why, because a child's sparkler or steel being ground is somewhat similar, but there's something special about steel in a forge.
Those damascus barrels . . . . I have no idea how much carbon is in something like that. I'd ask Harley Nolden or Jaeger who to ask about the steels used.