She might run nice until that magnet comes loose at WOT. JB Weld might work for a high stress application like this if you have a pristine surface to adhere to, but any oil or debris that's deep in the pores of the flywheel casting and magnet just weaken the bond. I'd definitely invest in a new flywheel if you don't want to risk that magnet becoming a projectile and doing damage to the machine, or anyone who might be around it when it lets go.
Also about your starter issues, you need a new bendix for it, it's the mechanism attached to the gear that throws it out when the starter is engaged. You might be able to find a new coil at a local small engine shop, especially if the coil was used on other more common Briggs engines, just take your current coil with you to compare it to what they give you.