"Jerusalem would have been jammed with people coming to the festival as commanded by God in the Torah. This is why there was no room for them at the inn." - Yeshua wasn't born in Jerusalem, He was born in Bethlehem! It was probably crowded because people were there for the census.
"...the Baby Yeshua was wrapped in strips of linen, most likely the strips of priestly garments that were in abundance during this festival because of their use for the giant lamps." - This is possible, however, Mary knew her time was close and would have been prepared for His birth with the proper supplies.
About Jerusalem's population during the pilgrimage feasts, the city in ancient times was much smaller than the city is today. The native population was less than 100,000. Jerusalem was surrounded by small villages and towns, Bethlehem among them. Bethlehem is less than 5 miles south of the walls of the ancient city and today it is difficult to tell where one leaves off and the other begins except for the signs and the border fence to the PA territory. It took all the accommodations available in these surrounding towns to house the people coming in for the pilgrimage festivals, the added burden of a censes not withstanding. Walking from Bethlehem to the Temple mount in that day would have taken less than 90 minutes. For information on the day to day life in Jerusalem during this time, see the works of Flavius Josephus. He was born in 33 CE and was present during many of these festivals in Jerusalem.
As far as the exact “materials” used by Mary and Joseph to wrap the baby Yeshua, we can only speculate. My purpose was to draw attention to an interesting possibility of the use of the strips of linen from the priestly garments. It is fitting that the King of Kings would be first wrapped in “priestly garments” at his birth. They were certainly available in Bethlehem since it is a city set aside for the Levites. The fact that they are the remnants of discarded and soiled garments is even more interesting in light that Yeshua would take on our “dirty laundry” so to speak at His death. Secondly the specific use of the term “spragnoo” in this context is as a noun and not a verb. It is in reference to a specific thing and not an action. Again, this is only speculation, but the cultural and linguistic context of the passage is interesting.