Mike, If you ride directly north out of Taos to near Alamosa like Jamawani and I did you are already east of Monarch Pass. Monarch would be a fun side trip but will add several days to your trip and lots of climbing. From Alamosa...
77 miles to Poncha Springs direct... one stiff climb, no Monarch Pass...
161 miles taking Jamawani's route... Saguache, CO114 to Parlin, then leave his route and turn east over Monarch Pass...
224 miles over Slumgullion and Monarch Pass. I deleted this suggestion from my original post when I added up the miles. That said, either Slumgullion or CO114 options would be fun side trips if you have the time and energy.
Perhaps you have a totally different route planned north from Taos.