My suggestion would be to make the vertical or horizontal strips "glow" and the winning way symbols flash or receive a highlight when indicating each winning way. It makes it easier to see the winners. When all the winning way symbols get highlighted the same way all at once, it is confusing to determine where the winners are, and to confirm the correct payout.
I would recommend against the "two stage" payout model. it is slow, and cumbersome. I think players would get confused and forget if they are on the first or second stage of each spin. I'd recommend spinning all the reels simultaneously, but allowing the player to "stop" the reels either individually by touching each one, all at once, or one side at a time. This would give the player an "illusion of control", which I think is appealing, even though the actual final positions were already determined randomly when the player pressed spin.
If that is not feasible, spin them all at once, but reveal them two strips (one vertical, one horizontal) at a time beginning in one corner and moving to the opposite corner.
America is all about speed. Hot, nasty, bad-ass speed. - Eleanor Roosevelt, 1936