Looks like what the OP is looking for can be done at AppBrain, using the
&sort=popular URL parameter. See e.g. this example search for file sync: First result page mosly holds apps with 10k+ downloads with a good "internal rating" (they have their own "rating number" in addition to the playstore rating). Checking some, they seem to have 10k+ ratings on GPlay as well. Additional filtering is possible for free/paid, new/updated, app2sd, reduced price.
Though not being exactly what was asked for, I guess it's pretty close. Another good result list can be obtained with the
&sort=highest-rated variant, which seems to sort by playstore rating: "file sync" by rating.