Your bow is going to be sticking up way over your head when you get on a horse with that pack on your back.
I still maintain that bows & horses do not mix. I hunt off of a horse during rifle season. I can tell you first hand that horses are hard enough on rifles. I would not even think of carrying my bow on a horse in a scabbard or on that pack that you ordered.
The only way I will pack a bow on a horse is in a good hard case as a top pack.
I guess you could bring two bows with you? Leave one ready to hunt in a good hard case. The other you could put on your new pack.
I own horses and know from years of experience that you are just asking for trouble.
If I were going on the same hunt I would pack my bow in on a horse in a good hard case. Then hunt from camp on foot.