It appears you have the correct race and bearing so that shouldn't be it. When you say it won't stay on, do you mean it won't stay tight and is spinning on the crank?
The clutch to stay tight is dependent on the flywheel taper being exacting to the clutch spider. I would try this with the new spider, get some valve lapping compound put it on the taper of the crank, put the spider on and spin it by hand to lap the 2 tapers together, inspecting it once in a while to see if there lapping together evenly. If the lapping looks good, clean it all off good then tighten the piss out of it when you put it back together. I suggest a 3/8's impact to set it, then tighten it by hand tight as you dare.
It also sounds like you have been a victim of the common practice of listing sprockets to fit both the 152, 153 and 166.
As you found out the 144/152 sprocket won't fit a 153.
If you really want a .404 sprocket for it, let me know I think I have one for a 153 that I will not ever be using. I have 2 of these saws in Poulan colors and try as I might I can't bring myself to love these saws.