Hi Brian Courtney,
As you did not move to the UK until the end of March 2023, under the 'split year' rules you would only have to declare (in your 2023 return) any income received between the date you arrived and the 5 April 2023.
When completing your Self Assessment Tax returns in the UK, both you and your wife can claim any Foreign Tax Credit Relief due in(respect of any US tax already paid) in the Foreign pages (SA106).
As regards your question about Self Assessment 'payments on account', you may find the following guidance helpful:
Understand your Self Assessment tax bill