To the K27 question first. According to a 1927 Baldwin Locomotive Company magazine article on the D&RGW, K27s were used in freight service on the Chili Line with the T12s doing the passenger run. After the train became a mixed, the K28s took over.
The D&RGW employees tt of the Alamosa division for 1938 shows K36s and K37s allowed as far south as the wye at Barranca. I have no photographic evidence of a 36 or 37 on the Chili Line, but newspaper accounts and D&RGW records indicate that 36s were used on the line on rotary runs in the 30s and in 1941. One of Dorman's books shows two 28s at Antonito with the comment that they were just off a rotary run on the Chili line. Often the D&RGW would run OY down the Chili line to Tres Piedras, Taos Junction, or Barranca after or before making a run over Cumbres. As the 36s were allowed on the branch, it seems unlikely that they would take them off the rotary and put on K28s, but as I have learned, almost anything is possible on the D&RGW. There are several accounts in newspapers of engines being taken off of freights bound for Chama or coming from Chama and being sent down the Chili line to rescue the mixed. The line got most of its snow on the north end just south of Antonito. There are accounts of large engines being used on stock specials on the north end of the Chili line and once a special train with two freight engines was used to rescue a herd of sheep stranded around Volcano.