All the problems I have seen on the FL250 with points is dirt and metal particles from the recoil getting into the points, the dirt problem came from the owner not keeping the rubber boot in good shape that seals out the dirt and or not maintaining the gasket between the recoil and the
Engine I use to take my recoil off once a year and inspect it and blow out the area with compressed air never had any ignition problems.
On a side note my 1955 IH CUB tractor has points dad bought this tractor in 1974 we have never touched the ignition on it, runs perfect, has spent the last 15 years setting out in the weather, have another 1970 IH Cub bought it 7 years ago havent touched the points on it, it sets out in the weather about 6 months a year.
http://www.pilotodyssey.com/PO/viewtopic.php?f=2&t=1349 Points are good and trouble free if you can keep them clean now is probably time to pull the flywheel and clean everything good then seal it up good.
Can you still get a new rubber boot for the recoil?
Most local dealers will have a flywheel puller for 10-15 bux
https://www.google.com/#q=fl250+flywheel+puller+