Here is a pic of my floor plan in the area

The rule of thumb I've always heard is that the minimum space behind a chair should be 3', optimal is 4'. I think you probably have room on either the short wall or long wall, especially if you can off-center the table a bit (ie. light fixture) -- you've got about 4 1/2 feet the whole way around the table without a sideboard, so if the sideboard is 18" you are right at the "acceptable" minimum

Is the light fixture dead center in the space, or do you have some flexibility with that?