This sentence is difficult to explain unless you are familiar with Japanese cultures as background. Anyway, I gave it a try. 床柱を背に=床柱を背に向けて This literally means to turn ones' back to a pillar of 床の間. Actually this means the person is the guest of honor, or high-ranking. My translation for the whole sentence would be: The person doesn't have a gourmet habit, acting the lord. Please refer to the followings: 床柱(とこばしら） is a pillar of 床の間.（とこのま） 床の間 is an alcove of a Japanese style room where flowers or other decorations are displayed. In a Japanese style room, 床の間 side is seat of honor and the guest of honor sits with one's back facing 床の間. 振った＝＞振る= to behave like, to act 食道楽 is one of hobbies or manias that means to be enthusiastic about eating delicious foods or cooking foods and take it as something one lives for, or someone who do those. 大尽 is a wealthy person. Somehow I feel that my translation isn't good enough, but I hope this helps you!

床柱(とこばしら) is an ornamental pillar not for structural functions. Sometimes people spend a lot of money on it. As Selly-san said, “床柱を背に(座る)” means the person seated there is the honor of guest or the key person in the room. Here is a link to a picture of tokonoma with tokobashira: https://pbs.twimg.com/media/CQhuPtYUkAQgb0U.jpg:large

ただの「turning one's back to the pillar」じゃないか？