Mine with that throttle also work in the wrong direction (ie pull up to rev up, push toward engine to stop).
My starting method is:
Fuel on, press and hold the tickler until fuel squirts out slightly
Tilt the mower onto its left wheels for about 5 seconds (about 45 degrees) - this dribbles a bit of fuel out the top of the main jet into the intake. I have found they start a lot easier this way.
Then set throttle about half and pull the cord.
Put back to idle for a few minutes to warmup and then go
