Are you refering to the book written by Fr. Demetrius E. Wysochansky? I currently have that book, having checked it out of a seminary library.
Yes, many of the icons that I have seen of Saint Josaphat depict him in Latin vestaments-with red cap even!
The icon that I described above came be seen on page 282.
I too have not read of any association that Saint Josaphat had with the Pochaiv monastery.
I am fascinated by your statement that the Basilians renamed icons of Saint Job as that of Saint Josaphat. I am curious to see the icon that you mentioned.
The icon I mentioned above though is that of Saint Josaphat. He is depicted holding the staff of a bishop. Saint Job was hegumen of the Pochaiv monastery but not a bishop.