Need I mount my wheel flush to the top of my fork ends?
The QR interface is designed such that the axle is fully seated in the dropouts before engaging the QR.  The QR engagement should be firm, but it is not designed to hold the wheel in the way you describe.  Dangers of trying to do what you suggest are:


Severely over-tightening the QR (which you may need to do to keep the wheel in place) could potentially result in QR breakage. If the QR breaks there will be nothing to hold your front wheel on and there is a very good chance you will end up in a bad crash.
If you do not seat the wheel, it is easy to accidentally clamp on an angle.  Given you want to clamp a fair ways down in the dropout it is easy to get really off-angled if you are not paying attentions.  As in (1) if you are severely over-tightening this could damage the drop outs and contribute to problem (1).
Even if you can get this to work, 3mm of clearance is still incredibly tight.  Tires can expand and contract with temperature and speed (meaning this clearance could start to disappear) and small debris picked up by the tires could result in a jammed wheel (briefly giving you the ability to fly).


If something does go wrong my bets are on (1) or (3).  The short of it, is that your frame simply isn't designed for 28mm tires.  This is the issue with short reach caliper brakes (now what most define as standard reach).  Frames with mid-reach caliper brakes can support tire sizes up to around 32-35mm depending if you want to run fenders as well.

Unfortunately, the N+1 rule has struck again...