You can try supporting the front of the rifle under the hinge pin instead of out on the fore-stock. Also free-floating and bedding the fore-stock should help. Allot of Handi's won't shoot well when supported under the fore-stock. Changing your load/bullet/velocity combination can tune out at least some of the vertical. I also speculate that the tighness of the buttsock could be an issue in vertical stringing.
Good shootin'
McLernon