Had an 066 with the same problem. Changed the coil. No jerk back now. Have an MS460 here with the same problem. Just enough slop in the keyway let me retard the timing a hair. Seems to have minimized the jerk back quite ait but it still wants to kick when it gets hot. Luckily it has a decomp. Not so lucky with the 066.
If you look at the coil closely on that 440 you may find it has scrapes and gouges (or even bent laminate) from coming in contact with the flywheel somewhere along the line. To make sure it's actually a timing issue giving you grief, pull it over with the switch shaft in the off position or pull the plug wire. If it still kicks back you've got some mean ass compression! You can also try pulling it over to just
past TDC.
Then give it everything you've got with a little more momentum on your side
before TDC. Seems like we typically tend to pull a saw over to right before TDC before giving it the main yank. Just sorta unconsciously natural as we make sure the pawls engage er somethin'..., I guess?
The coil is a 0000-400-1300 for both the 038 and the MS440. Used on everything from the 024 through the 064 and should be easy to come by. Aftermarket knock-offs are like 10~12 bux if you want to try that route instead. You can use your 044 coil for testing the 038 and MS440. They
should be the same coils, though not all 1300's look exactly alike. Obviously ensure the flywheel is correctly aligned and the air gap is within tolerance.
Had a Mac Super250 that gave me similar fits with compression and kicking back. Ignition was fine, just had boatloads of compression and I couldn't pull it over enough to draw fuel and fire. Looking back on it I'm guessing it was oil in the case from sitting so long. What got me over that hump was to prime through the plug hole until it stayed running enough to burn off the residual contents in the case. Still great compression but I can at least pull it over now!
Anyway, good luck with it. Be interested in what you find.