Hello, and welcome to TMW!
My first thought on reading your post is that you may be trying to reinvent the wheel. If your goal is simply to get some tunes on your bike, there are dozens of prepackaged, baked and buttered systems available to you, especially if you wear a helmet.
But, if it's more just a fun DIY project that you're challenging yourself with, I understand. If that's the case, I think your biggest hurdle is going to be output. I'm unaware of any Android devices that meet your specifications that have an output any more robust than a stereo headphone cable. One exception might be a device that can send audio via Bluetooth, in which case you might be able to use something like THIS
For the device itself, I can't see any reason not to just use a typical Android smartphone with a copy of the "RocketPlayer" app. That will simplify all your mounting solutions, you can move media back and forth via SD card or cloud apps, and depending on the model you select you can get pretty good weather proofing. For a remote, I'm sure there's a multitude to choose from. If you have the space in your cockpit you could also consider a smallish tablet. If you're 3D printing your enclosure that might be a fun thin to integrate.
Getting power to all these devices will be dodgy, but it always is. Let us know what you come up with!