Hi Bob;
Most (all?) hi-press fuel pumps have a built in check valve so this can be eliminated. Your transfer pump from the aux. tanks, I'm assuming a Facet pump? In this case, while they don't guarantee no backflow, it has been my experience that they hold pretty well, so a check valve could be eliminated here as well.

As Finn already mentioned, you can't have a "T" that draws off of 2 low wing tanks at the same time. You need to be able to isolate them. For the same reasons I would suggest that you also don't have an equalization pipe, between the main tanks. I would consider this be a failure point, as that pipe could lose all of your fuel, in a very short amount of time if it ever became compromised.

Another point to consider is that if you are planning on using Tracy's EC2/EM2 combination, then you don't need fuel flow transmitters. There are many other reasons to go with this, but easy fuel flow monitoring is a good one.

I've been discussing the removal of my header tank with Ed and he has pointed out the new returnless fuel systems on some newer vehicles. I'm closely examining them to see if there is the possibility of using this concept in my plane. if it works it would simplify fuel system design for us.