Hi y'all - I'm by no means an expert or even an experienced
Systematist, but I teach this movement to patients as a fundamental
posture/form exercise - I'm surprised at how difficult many people
find it. The heels come up because most people use their calf muscles
for the support and structure that their tendons and ligaments are
designed to provide. (and because so few people are available to kick
us while we stand on one leg- Shame..)

From my experience (and I'm a rank beginner in Systema- so please
accept this as an opinion, not the Gospel) my advice is:

Definitely use the wall.. I can almost get my bum to the floor on some
squats but I still like to use the wall for form correction. I think
it's best to begin with the heels on the wall and only go down as far
as you can comfortably - and with the heels on the ground. Don't lean
on the wall, though -it's there to help show you where your body is,
not to provide support. Try to 'spread' your body onto the wall-
lengthen and widen your back.

When you come to the bottom of your comfort zone, wait, breathe and
wait some more. Then see if there's a little more movement. If there's
not, it's no worries- there's always tomorrow.

Experiment with the angle and position of your feet - and make sure
your knees are tracking in the same direction that they're pointing.
I've heard of people pointing their feet straight forwards and
parallel, I prefer to turn them out on whatever angle is natural for
how far apart they are.

Ad breaks are a good time to practice this. If you can hold at the
bottom of your comfortable squat for 6 minutes, you beat me.

There's a lot more to this 'simple' exercise, but I hope the replies
so far have been of some help.

Tim.