I would run the clutch off the ign switch. Use the A or L terminal to the pto switch. Should only be hot in the run position. I believe the dual circuit dc side will produce 7.5 amps @ 3600. Clutch will draw no more than 4 and you got 3 for the battery. Direct off the battery leaves an opening for problems. Like corrosion or leaving the switch on (for whatever reason). I guess the interlock system is not functioning?
Doesn't briggs show the pto switch wired off the ign switch?