Hopefully the pros will weigh in on the effective distance between sconces, but in the mean time, here's a pic of an off center sink with a wide mirror and sconces. Looks good to me. The sconces are larger than the ones you've shown so maybe that's the way to get more light when the sconces are spaced farther apart. Also, visually, the longer sconces look better to me. Re: the smaller sink, for my eye it's more important to center for the space between the wall and window trim vs. the vanity. Your photo shopped example looks good to me.

Is this the exact spot where the mirror will be hung? I'm only asking because looks like your current vanity is on the opposite wall and I want to make sure that the space you'll have for the sconces will be the same.

I would consider putting the two sinks on the same wall, and a separate makeup vanity on teh wall wall where the sink in question i located -- or in the bedroom if there's space. Then you have lots of reasonable options. Otherwise, no lighting from one side of your face. Do single mirrors with lights above, or keep the long mirror.

Look at the option of putting 2 large pendant lights over the table. Not necessarily this style but this spacing may work with what you already have