I don't believe there is that big of a difference in different brand small gas engines. And I say that, that because I have a Kawasaki, and took off of B&S oil recommendation for there full synthetic recommendation. So for the B&S owners, you can learn off of Kawasaki oil recommendation that they have 10w40, 40 and now even 20w50 in there oil recommendation. So yeah, 40 and 50 weights are fine for your engines. So with your pick, T6 5w40 would be my first pick if you want to use a full synthetic, Rotella 15w40 would be my first pick for conventional oil.
30 straight weight is the only one of your choice that is recommended in B&S oil recommendation, but just not a fan of that choice. If the 40 weights are so wrong, consider this, straight 30 weight is tons more thick at start up than 40 weight is at operating temperature.