I didn't have any starting issues for the first year I owned the clipper. At first, it was only when I was filling the fuel tanks - then it started happening randomly when I turned off the engine. Didn't matter if the engine was hot or cold, etc. Got to the point that I couldn't trust the clipper.
On the battery wiring, does your house battery charge from the alternator while driving? Or is it completely separated unless you flip that switch? Sounds like you have a similar setup to what I've got set up. Under normal circumstances, when I start the engine, the house battery is disconnected (via a delay switch) for about 20 seconds. Once the engine is running, the delay ends and the house battery charges off the alternator. If the engine battery is low or dead, I flip a toggle switch and cancel the delay and start the engine with the house battery.