I checked for a Saturday, figuring thinner schedule but less chance of flight delays and higher chance of empty middle seat. I made a mini spreadsheet of flight times for LAX-SFO LAX-OAK LAX-SJC BUR-OAK BUR-SJC and the return trips for all those. Then I picked a route. 5 segments was comfortable but 6 required some tight connections. I'll bet you can do 6 if you are willing to risk partial failure of the run or if you fly on a Tuesday or Wednesday and finish very late in the day.
You are a star. Thank you for all your hard work. I've now rebooked two segments that I had booked earlier with points. That leaves me 4 segments to fly which should be easy in one day.