The thing is... If you have a website, and you're selling DIRECTLY from your website, you are the one who controls:
1. Who you're selling to
2. The quality
3. Your reputation
If you want to have this whole exclusive thing, make people "apply" to buy your beats. If they are good artists, then you can sell to them and you'll keep anything associated with you as high quality. Obviously, you won't be reaching the mass market by doing this. But it's certainly a way of keeping things a bit more exclusive.
That's just an idea.
Also, artists on majors don't care as much as you think. Even the more "respectable" artists couldn't give two s***s if you're selling beats online, as long as their final product (their song/album) is of a high enough standard.
Obviously, you have to deliver your music to them in a professional manner and therefore you can just have two systems in place. The one you currently have (with your manager and the majors) and then the online beat store for the "mass market".
The most important thing is what it all means to you. How do you want your brand to be perceived by the general public? If you are in all the "low quality" places with a cheap price, you're not going to build a high quality or an "exclusive" brand. Make yourself hard to buy from/only to those in the know if you want to seem "exclusive" and vice versa.
Let me repeat: having your own website means you have maximum control of the platform - not like Soundclick.
Cheers,
Jordan