Kickback tells me it could possibly be the coil failing.
Wrong Quote... the flywheel key removal and set was the quote.... cannot remove the quote above???
I agree, your spark time is off, late or early
Take the flywheel off and ck condition of the key and assemble
Sudden stop, torque, can change the location, maybe it was assemble w/o the key
You are unsure of the history.
Here is a electronics coil... no points to consider.....
https://www.lilredbarn.net/Husqvarna-365-Special-2005-05-Ignition-Coil-and-Chip-s/49818.htm
Would be a better saw with electronic spark.... contact them to see if fit, look at your flywheel and note how many magnets you have .... written info on link states there are different ones. That maybe you issue also.
Compression test is important for 2 stroke... need min 120psi and could be up to 150-160
Take the coil off, or ground the spark plug wire to the body with a alligator clip or similar
No discharge can build up heat in coil windings from lack of discharge location
No mention of compression
There are also spark test lights that INLINE with the plug & coil... the flash of light shows if you have a good spark. One of the posters suggested the coil, maybe slow in generating spark or bad. Takes some time to develop the spark energy of 20K-22K range and then the points allow the discharge. This could be. Not a fan of points. The discharge is set by the gap in points the gap is set with a feeler gauge. I do not know what you gap should be. The coil to fly wheel magnet :gap" is set with a business card between and then tightened up. The mount is the coil ground and should not be painted should be bare metal. I also use a bit of copper anti seize so it does not get oxidation and keeps ground.
Can by pass the carb by putting 1/4 to 1/3 tsp of mix directly into the cylinder and pull then.
The most telling statement..... When trying to start the saw the pull cord pulls out of my hand.
This is the time of the saw, set by the flywheel key
Take off the flywheel and reset the key