The only way you maximize the benefits of this kind of shooting is to literally "KEEP BOOK" on every shot you fire doing this. Then, practice dry firing at home, and continue to lift weights, and practice getting into your stance, until the movement of that front sight gets less and less, and the groups at longer ranges get smaller and smaller. You always want to challenge yourself in practice- shoot at 100 yards, when you already know that you won't take an off-hand shot at more than 50 yards. As you gain skill as a off-hand shooters, then you can let that maximum hunting yardage creep further out.
When I am training shooters, I try to get them to shoot their guns at ranges well beyond whatever they think the gun's "usual " range may be. I will teach them different ways of holding a gun, to shoot smaller groups at longer ranges, both off-hand and using rests of one kind or another. I teach them to use " Kentucky windage", holding over, and off, and letting the dust kicked up near the target to tell them where to hold for the next shot to put it on target.
Once they relax, and begin to enjoy long range shooting, they find they are making shots they thought were impossible.What I am really doing is teaching them to concentrate on that front sight, or part of it, so they reduce the size of their errors at the longer ranges.
Then, I have them come back and shoot off-hand at some target at 50 yards, a more " Normal " range they are used to shooting. Their groups are almost always way smaller than they were before we spent those hours long range shooting. That is when I have them begin shooting at smaller targets- 4 oz. juice cans, or short mushroom cans, then 12 gauge hulls, and on down to .22 rimfire casings. Necco wafers, cracker squares, corn cobs, etc. all make great " exploding" targets that reward the shooter with a wonderful "HIT " when he holds his shot tighter. Then, when I have them do that slow-fire 10-shot group again for the " Book" at the end of the day, they are amazed at how much the groups has shrunk, and how little that front sight seems to move compared to what they remember it did the day or week before. I have them check " the book" they keep, and they now know why I had them shooting at such crazy long ranges with their guns. They also begin a life time of " Keeping book " on their shooting, just like any other bench rest shooter does. The only time they don't keep book is when they are "Plinking" to knock the cobwebs off their shooting skills.