Hi arrive :)
Hope I can explain this right. This is correct to the best of my knowledge (I'm a member of a US based adoption board and I've picked this up, but have no personal experience)
You can only adopt in the UK if you live here, are a legal resident at least, and plan to continue living here for some time afterwards. So if you are going to take this contract UK adoption is out. This includes international adoption into the UK as well as domestic adotion
In the US, you cannot do an international adoption, unless at least one of you is a full citizen. I believe Kaz requires both to be citizens but the rest only one parent. This is the rule of the US government/immigration department that handles foreign adoptions
For a domestic adoption within the US (through foster care or a private agency to seek a newborn baby) you don't need to be a citizen necessarily. To the best of my knowledge, you need to be green card holders (permanent residents). However any individual adoption agency could make a rule that at least one parent be a citizen, even if it isn't legally required by the state
Even if you were already legal residents in the US, 3 years may not be long enough to complete an adoption anyway, owing to the length of time adoption can take. First homestudy ,and you'd have to get clearance from UK crb check as well as US. If domestic infant, you have to be picked by an expectant mum, and there is no timeline to that. Could be a couple of weeks, could be 4+ years. And with the foster care system, you have to be a foster parent to stand a good chance of adopting a child under 7/8 without serious emotional needs. System is designed so FPs can take in a child, and then adopt them if reunion can't happen. Not like the UK, where adotion and foster care are kept mostly seperate. If you wanted to adopt and not be a FP, you have to be open to children with moderate-severe needs, and most likely aged 7/8+
I think honestly, your only option is to go for three years, come back and settle in the UK again before beginning adoption here. You don't have the time over there you may need