Sounds like the forend is too loose, not much you can do for it on the synthetic stock except replace the forend to tighten it up some, although a thorough bedding job including the stud would work to increase pressure on the frame. If you remove the forend and close the action and it's loose, it needs a new barrel, doesn't sound like that's the case tho, but sometimes it's hard to tell with the forend on. It may have other issues, bad crown, chamber, ect. Maybe the best option would be to contact H&R and make arrangements to have them fix it, ask em to cover shipping, toll free (866)776-9292.
Tim