I have very little experience in a SAYC framework as well as this sequence where a 3H raise would be NF (even playing non-2/1 I would much prefer this to be GF), so I guess the question of whether South should move on depends on what kind of hands North would bid 4H on and what hands would go via 4th suit forcing (and even after a 3C 4th suit forcing, if opener bids 3NT over 3C, how weak/strong of a hand would bid 4H). But nevertheless I have a feeling that South should pass 4H due to the lack of 4th suit forcing. Any time that North has weak trumps (say Jxxx or Qxxx) the 5-level is in serious jeopardy (imagine x Jxxx KQxxx KQx or xx Qxxx KJxxx Ax etc.) Any time that North has a minimum GF and control rich hand should obviously go via 4th suit forcing, say with xx KQxx Kxxx Axx or Kx KJxx Qxxx Axx).