I switched things around a bit for a better fit. I tested all the drains and found two problems. 1) leaks at the barbed hose fittings and 2) gurgling noises in the bathroom plumbing.
I fixed the leaks by wrapping the connector barbs with a few layers of black electrical tape. That was just enough for a snugger fit and something to compress for a tighter seal. I used the 1 and 1/4 inch flex hose which works great, but the are not a lot of options for connections that I could find.. so I improvised.
The gurgling, I think, is because I need a vent/air admittance valve by the trap under the vanity sink... which I may be able to get away without if I get the front kitchen sink line leveled out with no dips and air could draw from the air admittance valve there more easily.. I think air is being blocked by water staying in some dips like a trap.. I'll try that first and then the additional air admittance valve/vent under the vanity.
I also found that if I put a few gallons of water in the sink and opened the drain, water would back into the shower very slightly. I am assuming that is because all that water at once cannot all get down the smaller pipes into the tank fast enough and backs up some.... it does quickly drain out however. I am not sure what I can do about that other than not drain the front sinks so fast with all that water. In reality, they will only be a small stream of water unless I was to fill the sink for dishes.
I'll make a new (removable) bottom for the vanity than will cover the bottom I cut out to access the plumbing.

This is the type of barbed connectors I used. Not sure what else I could have used?
