Is it possible to run the Mist browser with an external ETH client like INFURA? Yes, I understand this may not be the decentralized paradise we want to get to, but I'd just be happy to run a browser for now w/o having to download the entire blockchain. I understand I'll have to trust INFURA and I'm willing to do that for now.
Also, you may want to try out Metamask, which is a Chrome plugin for connecting to Ethereum, managing your accounts, etc. (Metamask uses INFURA as a backend.) It's a faster UX since you don't have to download (and possibly sync) Mist.