I have no objection to "aiming our fire" mainly at the Assad regime - for the reasons you say and also because it is the force originally responsible for and driving the sectarian polarisation, quite deliberately. But that seems to me different from saying "Down with Assad", which implies that we want the currently dominant opposition militias to overwhelm the regime (which is what is on the agenda - soviets are not on the agenda right now, unfortunately, indeed there is not really a labour movement at all).
Remember that in mid-1917 Lenin, while arguing for militant opposition to the Provisional Government (April Theses etc) also opposed the slogan "Down with the Provisional Government" on the grounds that the only forces capable of immediately overthrowing it were the bourgeois counter-revolution. This changed later in 1917 when the soviets began in their majority to support the Bolsheviks and Left SRs and thus became capable of seizing power.
I am not comparing Assad to the Provisional Government, of course, but making the point that the immediate violent overthrow of his regime by the only forces currently capable of doing it would not be a step forward for the Syrian workers and masses.
At the moment - unlike two years ago - the only forces conceivably capable of forcibly overthrowing Assad are the reactionary Sunni-sectarian militias. We should not want that any more than we should want Assad to win outright. Instead we should aim to help workers, leftists, democratic organisations etc construct a "third front" against both sides. But a victory for either side would hinder, not help, that goal. Hence we should not say "Down with..."
So this is a disagreement about slogans, but there may be some disagreements of analysis underneath. Look forward to more discussion.