As you might expect, the spelling of hoosegow was not well established during its early years of use in the United States, and several alternative spellings vied for a place in the lexicon. For example, from "The Coming City Election," in the Coconino [Arizona] Sun (April 8, 1910):
Tom [Wagner, candidate for city marshal] is a pioneer in Northern Arizona and a big-husky that would (111 the office plumb full to the brim. Bringing malefactors to the "hoozegow" in lots of four or five would lie an easy matter for him and he would do it with a smile.
The same newspaper used the same spelling hoozegow in subsequent articles on March 27, 1914 and November 27, 2014, so this first instance wasn't simply an inadvertent typo.
A year later we have this instance from "In Lowell Courts," in the Bisbee [Arizona] Daily Review (April 12, 1911):
John Hellon pleaded guilty to being drunk and disorderly and was committed to jail in lieu of a fine of six hard iron bones. Timotio Sanchez will also be at home to his friends in the casa of his friend Constanle Bailey for six days for Timotio was "busted." ... Walter Neimi, Peter Hanson and Victor Ritner received similar sentences but being "there" with the dinero, paid their fines and escaped the county hoosgaw. The Lowell jail has not been tenanted for a week and during that time was put through a strenuous course of house cleaning so that the prisoners find themselves in a veritable parlor.
But the earliest anglicization of juzgado that I've come across is from the Orange [Texas] Daily Tribune, which uses the capitalized spelling Hoosgow in separate stories three weeks apart in 1903. Here is the instance, from an item headed "In the Recorder's Court" (August 26, 1903):
Signor G. Fernantura refused to pay a hack hill, landed on the driver, landed Immediately thereafter in the Hoosgow and, upon his appearance before Recorder Nemits, was first ordered to pay the disputed bill and touched by the court for $12.70. He won't do it again.
And here is the second, from "Hose Wagon Caught a Thief" (September 14, 1903):
The police were notified, the negro lodged in the "Hoosgow," and the chickens were returned to their rightful owner.
That same spelling appears next in a story from the same Bisbee Daily Record that gave us hoosgaw in 1911. From an item under the general headline "Cochise County and Bisbee Suburbs" (July 14, 1907):
The local officers got busy last night and threw out the dragnet, and as a result the justice court this morning was a very busy place. W. H. Bush was the first up, he was fined $6, which he paid. The next were seven swarthy complexioned gentlemen from the land of manana, and they were fined $6 each, but being without the necessary mazuma were led back to the hoosgow, protesting their innocence.
Other pre-1910 occurrences of hoosgow pop up in newspapers from New Mexico and Colorado. From an untitled item in the Tucumcari [New Mexico] News and Tucumcari Times (August 24, 1907):
Tucumcari is getting to be a town where the hobo has troubles of his own. A few nights ago Sheriff Street and the City Marshal put a quartette of confidencers into the the hoosgow and the next morning they were brought before the police court and fined $10 and the trimmings and told to hike for tall timber. The birds have flown. We would like to see the good work go on until the city is purged of this sort of varmints.
And from "Mike Keefe Gets Jail Sentence," in the Ouray [Colorado] Herald (June 12, 1908):
Mike Keefe, a well known local character, was up in police court, before acting Police Magistrate Julian Hulaniski, Thursday, charged with vagrancy. It seems that Keefe has been living with a woman of the underworld for some time, claiming her as his wife by common law marriage. He was assessed a fine of $100 and costs which he was not able to pay and a mittamus was issued and he is now in jail serving out his time . He will probably be allowed to leave town in a short time. While in the "hoosgow" he wanted company, he said, and wanted to swear out a warrant for another fellow for much the same offense. He is still alone.
The first occurrence of the word in an Eastern newspaper was in "Senor Battery Dan: Uses the Castilian Speech Only When He Finds English Inadequate" in the [New York] Sun (September 19, 1909):
"Police as a rule are not endowed with any 'savvy.' Twenty out of every twenty-five men who are put in the 'hoozgow' are truck drivers who are treated as criminals because a horse's head has been turned the wrong way.
The first Elephind match for hoosegow is from an untitled item in the Creede [Colorado] Candle (July 29, 1911):
Editor Harry Baker of the Creede Candle came over from Creede horseback Saturday, returning home Tuesday. The fact that the manager of this paper was off duty as marshall accounts for the fact that Baker did not spend most of his time here in the calaboose on a diet of poor bread and thin water. His conduct was scandalous.—Lake City Times. Isn't Kinney a peach? If the bread had been as poor and the water as thin as Kinney himself, we would have had a tough time had we lit in the hoosegow.
That all of these spellings began as attempts to anglicize the Spanish word juzgado is clear from the occurrence of the Spanish word itself in earlier articles in U.S. publications. One such instance appears in "A Bad Mexican" the El Paso [Texas] Herald (January 25, 1901):
A poor Mexican woman was unmercifully beaten with a stick by a man who was under the influence of mezcal in Monterey [Mexico]. The officers have been unable to locate the guilty party but are on his trail and expect to lodge the criminal in the comfortable quarters of the juzgado before long. The woman is horribly beaten and is not expected to live.
This example indicates that in at least one U.S. city on the U.S.–Mexico border, an anglophone newspaper editor expected his readers to recognize and understand the Spanish word juzgado in the midst of an English-language news story.