Chris from CA.
What's the best and safest way to shut down and restart the gen under load with the main utility being out? We also have a solar system with no battery back-up.

Turn off the breaker on the generator, wait 3 minutes or so for it to cool down, then hit the off button. 
To restart, switch to auto, the generator will start, wait a minute or two for warmup and switch the breaker back on. 

Or, search for my thread on designing my system to do this remotely from inside the house. It does require a smart transfer switch  and some additional hardware though. 
Birken Vogt
The solar system should not be connected to the generator output loads in any way.  It should be on the utility side of the transfer switch.  If it is not, fix it so that it is.

Good times coming up here in California.