Instead of foam board, I suggest using 4-ply alpha cellulose matboard for the support/filler board. It cuts easily and you can quickly sand the edges to avoid abrasion damage to the fabric. Nylon tagging is still a good way to attach it. Push the tool's point through the back of the mounting board, through the back of the jersey and through the 4-ply support/filler board. The support/filler board is what actually supports the jersey, and only a few nylon tags are required. Including extra tags to hold the sleeves in place, I usually end up using 10-12 tags in a full-size jersey.
I would recommend avoiding all adhesives for attachment of textile items. Nylon tagging is practical for sturdy, stretchy fabrics, such as the common sports jerseys of limited value, as the large diameter of the tagging gun's needle would not harm the fabric. But when you need to mount a garment that is fragile or finely woven, including antique sports jerseys made of wool or cotton, be sure to sew carefully using needle and thread.