When splitting the closing of hedged sdraddles into two orders you can also close the winning side in one trade (shorts and longs) and then close the losing side in another. I'll often do this when the stock price has had a big move - closing the winning side first in one order since its very sensitive to stock price movement with its ITM, and then closing the losing side whose price moves much slower.
I believe you can exit in one trade. But I've had better luck closing them separately, just my experience. You just can't have a naked trade. So for example, you either close the hedged straddle as one trade, or you must first close the strangle, then the straddle if you split it into two trades.