Page,
Wow, your post is eye opening! I have been with a small company for 8 years in a corporate marketing role; however, my position is anything but traditional. I don't office from the corporate office, I split time between being onsite and a home (as in my house) office. Now, I will say that prior to this position, I do have 10 years experience as a true PM. I have sometimes wondered if my current tenure will hurt my prospects in the future.
Microsoft template for a resume? Resume parser? I am a creative. My resume is done in Illustrator. I have a web portfolio. I also have my BA in Multimedia, Web & Graphic Design and Development.
With that being said - Skip the online application and network. If there is one thing I have learned in close to 20 years, it's this. Property Management is a small industry. Everyone knows everyone. If I recall, the TAA is huge and very active; Do they have any resources you can use? What about your ad reps or other vendors? Are any of them willing to offer a recommendation, contact or direction? Does the Apartment Association of Greater Dallas have any opportunities where you can get involved and meet some appropriate people?
Also, out of curiosity? What type of position are you targeting? Are you looking for a Marketing role or similar or are your trying for more of an onsite position? I can see how your credentials would be a little intimidating for an onsite role, but fail to see any issue with fitting into a marketing role.