That sounds more like a problem with the charger coil winding on the stator to me.
The Saturno FAQ tends to confirm the ignition coil is a 0.3 ohm one. I doubt David Chapion would have got it wrong as he worked for Piaggio.
It also gives the resistance for the charger coil. Check it as quickly as you can while it is still hot. The winding insulation may be breaking down.
Ignition - Workshop manual. page 17-2 to 17-5
Timing - 7deg (static). 30deg at 4500rpm. not adjustable.
Charger coil - part of stator. part no. 328239
Resistance test - 150 ohm + 10% (pink to green)
H.T. Coil - part no.321825
Primary res. - 0.2 - 0.3 ohm + 10% (white-lt.blue to black)
Secondary res. - 4.5 K ohms + 10% (white-lt.blue to H.T.)
Pick up coil - part no.328240
Resistance - 110 ohm + 10% (white-green to white-red)
www.gilera.org.uk/gilera/gens/FAQS.pdf
"Do not adjust your mind, there is a fault in the reality"
1957 175 Sport