Anyone have some thoughts as to whether an accelerated two year LLB in the UK + a one year UK LLM would suffice.

If a three-year LLB works, then one would think so since the years and subject matter are largely the same... but you never know, I suppose...

It will not. It's not only about the years, the content of the 3 years LLB degree needs to be similar to a 3 year American JD, ie the degree itself needs to qualify you to practice in England, you need to take the standard modules like criminal and equity and electives. an extra LLM is irrelevant for the BOLE in Albany. 

Anyone have some thoughts as to whether an accelerated two year LLB in the UK + a one year UK LLM would suffice.

If a three-year LLB works, then one would think so since the years and subject matter are largely the same... but you never know, I suppose...

I have taken: 
Torts
Criminal
Contracts
Property
Trusts& Equity
Foundations of Law
UK Public Law 1 and 2
Business Orangisations
EU Law
Intellectual Property. 
Are there any core modules I am missing? 

You needed to do the 3 year LLB of all of those QLD modules along with the electives. Sorry, the BOLE will not clear you. I know this from having helped a lot of other people through this. If you send in the documents to the BOLE, they will probably tell you that you can cure the deficiency with a 1 year LLM at an American Bar Association accredited law school. The BOLE clearance is free of charge. If you are already a licensed solicitor or barrister then you can go sit the California Bar Exam, maybe the Washington State Bar Exam as well although I am unsure about that. Hope this helps.

I have taken: 
Torts
Criminal
Contracts
Property
Trusts& Equity
Foundations of Law
UK Public Law 1 and 2
Business Orangisations
EU Law
Intellectual Property. 
Are there any core modules I am missing?