RE: Size comparison of parts for 1/20th scale and 1/13th scale
There are a number of suppliers of 1" scale equipment, intended for the 5" gauge ride-on market. 1" : 1 Ft =1:12, so they are very close to 1:13.7, or 7/8ths scale.
So are Doll houses - most are 1" scale! All those lamps, chairs, and rugs will fit your caboose!