I don’t know what he does but it makes no sense (to me...at this moment) what the manual says.....as long as the inverter can handle the surge of the component....then why would it matter which way you turn it on? I believe he leaves the inverter on all the time and turns his amps on and off via the amps.....his JC1+ amps have delayed start up using relays. I believe he leaves all his low level components on all the time....except maybe his 300B based preamp (got to conserve those expensive tubes). He leaves the charger plugged in and running except when listening......so he is always at full battery charge when he starts to listen.
I don’t know what you are talking about when you say "2 to three times your power needs". The inverter only supplies what it is asked. As long as the inverter is large enough, it will work. Now about sound....it could be a way larger than needed inverter will sound better....same with paralleling batteries......these things need to be sonically tested.
You need to have an inverter that will handle the SURGE turn on current of your gear. For instance, my 400 watt Goal Zero will NOT turn on my Purifi Class D amp that only draws 30 watts when idling......because the turn on surge of the power supply in the amp is way above the surge capability of the Goal Zero.....the Goal Zero shuts off when I try to turn on the amp......so, I have an AC switch on my amp that switches between the wall AC and the inverter AC. So, I turn on the amp with the wall AC and then I switch to the Goal Zero power. If I had a 1000 watt Inverter I am sure it could handle the turn on surge. Why would anyone buy an inverter less than 2000 watts (4000 watt surge)?.....They are sooooo cheap ($350 for a Giandel).