The mere existence of a Humble Bundle app made it a little easier to sideload all those APK files, but the quality of the app was seriously lacking. Well, now it's all fixed up and out of beta. The v2.0 update to the Humble Bundle app brings a new design and easier access to all of your purchased content.
There are a few screens of the old app down below for comparison. I think you'll agree that the new app is worlds better, even though it's getting Holo right just in time for Material. Still, the layout is much more standardized and you can finally see all the audio content you've gotten with those game purchases. Soundtracks can be downloaded to your device as either MP3 or FLAC (in ZIP files). If you've taken advantage of the Humble Bundle's ebook deals, those are available too.
The app includes settings for where audio and books are downloaded and offers to keep your selection in sync. I always had issues with the old app hanging and crashing in bizarre ways, but this one seems perfectly solid. Maybe this is a good time to grab that most recent bundle.
The old app