Took a bunch of comments to flush out this answer. You are in 'handwavy' physics here and if your audience wanted to, they'd probably pick these thing apart. If the audience is in for the fun of it...Star wars exists doesn't it? Will try to keep in that frame of mind for the answer.
Here is my solution:
Have the viscosity of ether related to gravity. A higher gravitational effect (lets say mercury sized or larger) produces enough of a gravitational effect to negate the viscosity of the ether (yes, the solution is hand wavy, but so are the properties of dark matter, why can't gravity effect how 'solid' the ether is). The end result here is planets and planetoids can keep an orbit, and you will still have your ether. Better yet, you'll have area's of extreme viscus ether between planets and in microgravity space. A little hand wavy, but it works...a gravity field applied to ether lowers viscosity to near 0. It's also possible to have the viscosity of ether related to the speed of whats travelling through it.
Detecting changes in the viscosity of ether over distances would functionally work as a gravity scanner...pick out large gravity objects by detecting a change in the ether...maybe?
This would also mean the gravity of earth would keep the viscosity of ether down so the moon is a viewable object and people can reach for the moon (maybe not the stars)? Satellites also remain feasible...and it would also mean that a plane couldn't just fly to the moon as the gravity of the moon and earth eliminate the thicker ether there.
And to continue along these lines..the suns gravity could then be explained on how to keep the sunlight reaching earth. You might have to bring earth significantly closer to the sun, but if the ether was thin around the sun you would simply have the planetary golidlocks zone close to the sun.
Remember that from earth only the sun, moon, and maybe venus at the right time of year is all that will be perceivable. Everything else will be blackness. Star light, star bright, I'll never see a star at night?
Comets and asteroids will be an odd phenom...they would slow down as they traveled (especially through deep space) and eventually slow to the point that they'd drift into other planets gravitational fields and eventual collision (maybe a moon?). Asteroid fields might not be feasible...same issue where they come to a halt in the ether and slowly collapse (our asteroid belt would go into the sun). Would there be a big change in Earths development if it was never struck by meteors? Your call