Why is my empty lap band causing food/beverages to get stuck?

Your band may have slipped.  You need to have an upper gi series, and have the x rays read by a bariatric surgeon.  There is a very good chance the band has moved.  Also, have a bariatric surgeon completely empty the band.  This may make your symptoms improved.  I know you said your band is empty, but I have been told the same by some patients and I end up removing one or two cc from the supposedly emptied band.  

This is a very common symptom for people who have their band slipped!
So you need to get an Upper GI X-Ray to evaluate the band. In that case, the best option is to remove your band and get a Gastric Sleeve. The Sleeve and removal of the band can be done at same time, depending on how bad your slippage is.
In regard to worsening the symptoms during stress, again that could be a sign that there is something wrong with your band. An Upper GI X-Ray and possibly Endoscopy is all you need to evaluate your stomach and plan a definitive treatment.
So try to get the Band out and get a Sleeve!!!

Having the lap band long term is associated with several complications- these symptoms could be from band erosion into the stomach wall, severe reflux, or band slippage- a band erosion or slip could be potentially life threatening.  I recommend going to see someone ASAP and get imaging done.