There is a fuel solenoid attached to the carb. body . It closes when you turn the key off and opens with key on and running/cranking . There is a time delay module that often fails on the 425 and causes intermittent run problems . That module is only about 25-30 bucks from Deere , and is where I would start if trouble-shooting/throwing parts at it . It just may solve your problem . This is the thing that allows the motor to run for a couple seconds after you turn the key off , to allow the tractor to burn out fuel stored in carb. float bowl , and prevent back-firing at shut down .
It's definitely worth a try to start with , if only to keep from pulling your hair out trying replacing other things first ; then to find out many hundred dollars later , that a cheap part would have solved your problem in the first place .
This advise precludes a good thorough inspection / cleaning of carb. of junk that could also be causing problems . Hoses to carb. can deteriorate letting little bitty chunks of rubber to get lodged in jets/passages that will keep returning unless dealt with . Filter clean ??
Side note : Don't be afraid to tear the carb down with-out a gasket set , as you can usually re-use them ; if you are careful when dis-assembling . Also note that the 93' came with a carb. vent solenoid that was soon replaced with an up-graded carb. that had the main jet fuel solenoid mentioned in the first paragraph . I should have mentioned this first ; forgive me . Lots of early models such as yours where plagued with problems due to the vent solenoid , and most have only been fixed officially by changing to the up-graded carb. You should first determine if your 93' still has the old system , or if it has been changed to the new style "FIX" carb. from Deere . Until then , all attempts to diagnose will be mute . Sorry .