I'll second the use of the supreme slider. That helps a lot.
Also, practice the smooth curves and even spacing by doodling with a pen on paper. I do this at meetings or when on the phone, and it really does help my brain/eye/hand connection.
I also find it helpful to visualize a dime or a nickel and make my curves around my imaginary loose change, keeping it close to the same size. I do a very basic stipple pattern of 3 nice curves to the right, then 2 down, and 2 to the left, then three down, and repeat. Over time, you work in a lot of variations on that.
With the BSR -- which mode are you using? I started with BSR 2, without the foot pedal, and going solely on speed of movement. As I've progressed, I find I like my results on BSR 1 with the foot pedal -- I personally have better control and more pleasing results.
If you haven't taken all your classes yet, that may help -- having an instructor show you the various modes and methods of using the BSR.
And finally -- it's really not hard, but nobody is going to deny that it takes practice. Your sandwiches destined for stockings approach is a good start, but keep going. The freemotion quilters who do the amazing work we all admire most likely put in time almost every day.
RST