This has been discussed several times: whenever you have invisible AIs, it's because they aren't FSX native models, but converted from FS9 (their .MDL is compiled with the FS9 SDK), and are not compatible with airports that use custom runway textures. This happens to many addon airports, not just FSDT's
UT2 models should be FSX native but, if you downloaded other models which weren't, even if you used UT2 to assign them, they are still FS9 models, which creates that issue.
The solution is either switch the "Airplane Cast Shadows on Ground" option off in the settings, or using AI models that has been compiled using the FSX SDK.