Block /wp-admin for non-admin, logged-in users

I am working on a BuddyPress site, but this issue is not really specific to BP at all. I have used Better WP Security plugin (http://wordpress.org/plugins/better-wp-security/) to change the "/wp-admin" URL (and a bunch of other security measures). Now, when a non-logged in user goes to "mydomain.com/wp-admin", it shows a 404 error (based on my theme's not found page). When a non-logged in user goes to "mydomain.com/new-admin-URL", he/she will be redirected to "mydomain.com/wp-login.php?[my-secret-key]&redirect_to=/wp-admin/.

The only issue is that since my website is a BuddyPress one, most of the users will be logged in (through my front-end login form). When a logged-in user (not matter what their role/capability is) goes to "mydomain.com/wp-admin", they will be taken to the Admin Dashboard. Currently, I have used Easy Blogging to theme the Admin Dashboard to have absolutely no menu items (except logout) and force all users except administrator to go to the Easy Mode dashboard (a part of plugin). But still, this does not look good and this quote below explains exactly why:

it just doesn’t look good if someone could go inside the “admin panel” of Facebook, for example (imagining such a thing exists :wink: ) it has nothing to do with your theme design, surely not customized, etc, etc. Even if they could not change any configuration (always talking of a social web with no “blogs for everyone” as is my case too).

-- juanmaguerrero
http://buddypress.org/support/topic/disable-wp-admin-for-normal-users/

Basically, I want to prevent the general user from knowing that they are on a WordPress site. I have taken a lot of measures to do this, but this issue is still in my way. I imagine having a solution like below:

When a non-admin, logged-in user attempts to go to "/wp-admin", it displays my theme's 404/page not found message/page (http://codex.wordpress.org/Creating_an_Error_404_Page).

That's just the kind of setup that I was hoping for, but it's not the only option. If someone thinks of something better, be my guest and post how to follow through with it — just keep in mind that I don't want users to even get a glimpse that I'm hiding something at "/wp-admin" (that's why I like the 404).

Anyways, please respond as soon as possible. Thanks in advance! It's really appreciated.