I don't know your criteria, what you want. I don't even know what you mean by EE, there is no specific definition as EE's are not a recognized breed. That's not you being dumb, experts disagree over definitions. To some people if you cross two different color/pattern Ameraucana so you get an unrecognized color/pattern that is an EE. To others it's still an Ameraucana, just not a recognized color/pattern. Does an EE hen need to lay a blue or green egg to be an EE? Some people say yes, others say that one of her ancestors needs to have hatched from a blue or green egg and she is still an EE.
The difference in an EE and an OE is just egg shell color. Even then, different people have different ideas on what shade of green an egg needs to be to call it and olive egg. That can change during her laying cycle too. The later the hen is in her laying cycle the less brown she often puts on an egg. So some eggs are darker when a hen firsts start to lay after a molt than just before she molts, often a significant difference. Since there are no accepted definitions of EE and OE that everyone agrees to, it gets complicated pretty fast. You don't know what someone else means by those terms. It could easily be different from what you think it should be.
Egg shell color genetics and feather color/pattern genetics need to be looked at as two totally separate things. Basic egg shell color genetics aren't that complicated though when you start talking about exact shade it can get messy. There is one gene pair that determines the egg shell base color. This is not a sex linked gene pair, both the hen and the rooster contribute equally. Roosters don't lay eggs so you can't tell by looking what they contribute, but Blue is dominant. If just one of the genes at that gene pair is Blue or if both are Blue, the hen will lay a blue egg. If neither is the dominant Blue the base color will default to white. That is pretty straight forward. By definition your Ameraucana should have nothing but the Blue egg shell color gene so both males and females will contribute a Blue shell gene to their offspring.
Brown and Green egg shells are just brown added to the base colors. This may help you understand that.
Blue + no brown = Blue
Blue + brown = Green
White + no Brown = White
White + brown = Brown
There are several different gene pairs that affect the shade of brown. Some are dominant, some are recessive, some only act if another specific gene is there, at least one is sex linked, and one can bleach brown to white. Exactly which ones are present (if any) determines the exact shade of brown. That's why you can get so many different shades of green or brown. You don't know which ones are actually present by looking so you can get some surprises in the shade the pullets lay.
If you want an olive colored egg, your best bet is to cross one of your Ameraucana or Legbar roosters over the Marans or Welsummer hen that is laying the darkest brown egg. There is no genetic link of feather color/pattern to egg shell color. Some Birchen Marans will lay lighter or darker eggs than other Birchen Marans, let alone your BBS or Welsummer. To me the best way to determine which hen or hens will contribute more dark brown egg shell genetics is to look at what they are leaving in the nest. The reason I suggest an Ameraucana or Legbar male over a brown egg laying hen for an Olive egg is that roosters do not lay eggs. You could use a Marans rooster over an Ameraucana or Legbar hen and probably get something OK but you don't have a way of comparing which male contributes the darkest shell genetics.
That's a lot of typing but if you boil it down it's fairly simple. The base color is straight forward as only one gene pair is involved. The actual shade of brown is more uncertain because there are more possible genes involved. Feather color/pattern genetics gets a lot more complicated because there are a lot of gene pairs involved. If you are not going to show them or sell chicks or hatching eggs of a specific accepted color/pattern then the only reason it matters is your personal preference. Personal preference is really strong and I don't know what yours are. So I'll quit here.
