They are real common parts and simple enough to replace. The mower is made by Husqvarna if that helps you source parts. You can get the entire spindle assy or simply the shaft kit. Inspect the legs of the spindle to ensure that they are not cracked. To replace the shaft, only remove the top pulley nut and drive through the housing. Removing the bolts that retain the spindle housing to the mower deck can break off the bolts- which require that you replace the assembly. Install is in reverse order -remembering the spacer washer under the pulley. Speaking of which, before you order parts, look at that pulley to make sure it turns true and that the spline in the center of that pulley is not spun. WIth all this being said, you can sometimes save these by carefully grinding the burr off the star until you can get the blade to seat.

Thank you tomplum for the excellent reply!

I showed the pic to my (adult) son after posting this, and next weekend we are going to try filing/grinding down the burrs and see if we can get the blades back on tightly.

If that doesn't work, the remainder of your advice should prove to be very helpful.

You bet. Before you get too far into it, rotate the shaft watching the bottom carefully to ensure that the shaft is true to start with.