This looks like a classic case of compiling with different flags.
The two that spring to mind are HXCPP_VISIT_ALLOCS and HXCPP_API_LEVEL. There could also be some debug flags.
When you compile the other cpp files, you can see the "g++" command line, and the defines that are on that - you will need these if you want to interact with generated header files directly.
The alternative is to write some custom api code, and get this compiled at the same time as the hxcpp code. This api would contain only types that do not refer to the haxe headers directly, and add a "glue layer". External code would then interact only with this API, and therefore be isolated from the hxcpp compile flags. This might be quite some work, but there is an interesting option of using macros to generate this API, which I think would be pretty nice.
Lastly, you could write a build.xml file for your custom application and get hxcpp to compile up your whole project with the same flags at the same time. This may avoid the need for additional makefiles etc.
Hugh