For some reason, Jersey patterns tend to have an elongated eye, I feel your pain. Jersey's are one of my favorite axe patterns. Personally, I would not hang that head on that handle, at least so long as you intend to actually use it. The last Jersey I hung also had an elongated eye, but I found that
House Handle Co. turns their hafts for single bits that will fit that. I would take some measurements on the bottom of the head and compare with what you find for handle eye size. The eye measurement of 13/16 x 2 7/16 worked for my recent True Temper Kelley Perfect below: