Aren't we "brainiac" enough for you Paul!!


OK I'll go out on a limb....
Basically playing with the HDOP or Min Sats doesn't matter unless you have crap data or you make the criteria too stringent (ie you must have 500 satellites locked!).
For the stop speed and alpha issue, its probably because when you stop (jump off) your speed doesn't go to zero. It fluctuates because the satellites are moving, check your tracks and you'll see "stopped" speed varies up to and sometimes over 1 knot. This is then worse if you fall in on a gybe and you move the board around etc, then your "stopped" speed could be over 2 knots! So if your stop speed is set too low, as your actual speed fluctuates above and below your set "stop speed", realspeed may think your alpha has stopped and started 10 or 20 times while you get back on the board. Mal may be the only definitive answer for this one, but a stopped speed somewhere from 7 down to 2 knots seems to give the same result. It also matches KA72. Also if your top 5 gybes never drop below or equal your stop run speed (also assuming you also have a very low stop run speed ie < 2kts), you will never see this problem in your tracks (if only

)
So although DHOP and Min Sats shouldn't matter, I use
Time Threshold = 200 (default)
Speed Threshold = 50 (default unless you're damn fast!)
Acc Threshold = 7kt/s2 seems a reasonable default, though I doubt 5kt/s2 would have too much affect. How fast are the start of your catapults?? If you set it too low the accelerations in gusts will be marked as invalid.
Stop Run Speed = 7 (However any value down to 2 knots should work)
Doppler Error = (Not sure but I've never seen it go above 0 for my GT31)
DHOP = 4 (default - reasonable upper limit, could even be lower)
Min SATS = 5 (reasonable minimum, usually we get 8+ in Perth)
Decc Threshold = Similiar to Acc, 15 seems reasonable and would 10 really make a difference? 10 is similar to jumping off your board at 10 knots, so anything above that you definitely don't need for your results.
Stop Angle = 90 (default for a change of direction)
Paul if you are having problems with a higher Stop Run Speed, send me the track and I'll have a look.