The absolute best advice I can give is to get an account on last.fm if you haven't already. Once you start working up a play count of the music you already listen to you can go through the band pages to find similar artists and get recommendations. I've expanded my narrow scope of about 60 bands in 5 years to over 200 more in about 10 months.
It's too bad you don't like the weirder side of Zappa as much because I have about a dozen recommendations
People who like Zappa tend to like Mike Patton's projects like Mr. Bungle and Tomahawk, and other avantgarde-metal bands like Dog Fashion Disco, Polkadot Cadaver, and Tub Ring. But the Flo & Eddie era is more like a humorous take on classic rock and blues, so I don't know. Captain Beefheart, Tom Waits?
Yeah, Lush is considered dreampop, or "shoegaze", which is a genre I still don't fucking understand. My Bloody Valentine is similar. I would check out M83, Beach House, and The Brian Jonestown Massacre for starters maybe? If you like the electronic side of things you could try Stereolab or Broadcast.
I'll throw up some links later when I get the chance.