Your log file shows you have a custom GSX profile for KDCA you made yourself.
However, you log also shows you weren't at KDCA when you made it, because ( according to your log ), you started at KDCA, then you moved to KBWI, then you moved to KEWR so, it's difficult to say what the problem is, because I can see GSX jetways being loaded, but they seem to be for KBWI.
Please go ONLY to KDCA and check the scenery customization page what does it say about jetways.
A common issue with 3rd party scenery developers and SODE jetways, is they use names not confirming to the AFCAD standard.
This might work with SODE only, but in order for SODE to work together with GSX, the SODE jetways MUST be named using the precise, exact, standard naming convention of the AFCAD. This won't obviously limit or prevent the developer ability to give the jetway name a "friendly" name, which can be anything, but the name *itself* MUST be confirming to the AFCAD standards. Lots of 3rd party developers don't fully understand this, so their SODE jetways works only with SODE, but not with GSX.