Anyway, I do believe you are right and I had misremembered {bIQtIqDaq vIghoS}. Thanks for pointing that out. So, depending on the prefix, the {-Daq} is optional. I was wrong about that. I personally think that {bIQtIq vIghoS} is stylistically preferable to {bIQtIqDaq vIghoS}, since it is less ambiguous, given that there could be some implied course that doesn’t involve the river if you include {-Daq}, but that’s just a personal opinion carrying no more weight than anyone else’s opinion.
It's not exactly optional. There is a difference: bIQtIqDaq vIghoS is "somewhat redundant, but not out-and-out wrong."
So your choices are to not use the -Daq or to use the -Daq and be somewhat redundant.
And it's not really dependent on the prefix. It's just that the
prefix makes it clear whether you're talking about an object or a
noun that comes before the object-verb-subject structure. In TKD
the difference is shown without changing any prefix: Duj
ghoStaH It is approaching the ship versus DujDaq
ghoStaH It is approaching toward the ship. Using an
example without an illustrative prefix is just harder to follow.
-- SuStel http://trimboli.name