That is indeed an expander. PB Blaster is another agent useful for loosening corroded parts, but anything labeled "penetrating oil" is better than nothing. Put some in from above, let it sit for a day, then flip the bike and put some in from below for another day. I cannot tell from the photo if the wedge is sitting on an internal ledge in the steerer. Hopefully not, as that is going to make your task extremely difficult.

If the steerer is not stopping the wedge from traveling further down just get a rod long enough to reach it from the top of the sem, put the fork blades on a block of wood on the floor, and give the expander several good whacks. Hopefully that will knock it down enough to release the pressure on the stem, but the stem may still be stuck from corrosion. if so the best way to get the leverage necessary to free it is to find a mechanic's vise large enough to hold the fork crown (padded) in place, clamp it in, and then twist the stem back and forth to loosen it. You can usually also place a block of wood on top of the stem and give it a few whacks once the expander is loosened, but yours appears to have almost no space between stem and locknut.

If the expander cannot move down further you are indeed "stuck." If you try to move it from the bottom you just move it further into the stem. If the stem merely has a recessed area for a bolt, with a small hole, you could drill out the expander and then try to use a rod to pound the stem out (LOTS of work). For me at that point it would not be worth it except for a high-end frame, which is not the case.