You need to pay attention to the amps on the battery charger. (right at the battery charger output) It's the supply that has replaced the engines regulator and stator. Their can be a additional DC amps between the ammeter you are reading NOW and the supply. (in the wire loom harness before the ammeter) Summary: monitor the DC amps coming out of the battery charger.
If it is still is only showing same or low amps right at the charger output the regulator itself will be the suspect and need tested. It could be possible for a voltage regulator if the full wave type to have one bad rectifier and sending OUT both AC and DC and this would overload the AC stator voltage's output and not quite enough current to open the 20 amps fuse but burn out the stator. (when you see your stator volts drop from 30vAC to 8 it's overloaded and going to smoke fast, which you have already witnessed twice)
Is your regulator the three wire type? (two wire for the stator and one wire for the B= out and a ground block?
(can you post up a picture or part number of your regulator you are using????If this is type regulator (3 wire with ground) we can test with ohmmeter by comparing both white stator wires to the B+ out wire. Both white wires should test EXACTLY the same when using Ohmmeter to the B+ output. White wire to white wire at the regulator should read open or high amps, each white wire to B+ out should read same both forward and reversing the Ohmmeter leads.
Most generally 24volt control transformers @ around $15 are 40VA, 40watts/24volts=1.66666AC amps, so fuse at not over 2 amps to prevent overheating.
But wait few days and maybe Murphy will leave you. He has been causing me several different problems on a Briggs engine. (different things fail daily but on different days on this engine, carb one day, magneto next day, valve lash adjuster came loose another day)Not all same day, about time I think it's Ok down it goes.
Patience.