Thanks for your insights. You are right, I have a long 23h connection, not a layover. However, I still don't want my bags checked to ALG ;-).
So your guess is BA will check for the visa in the USA? Showing them a ticket from London to the EU won't help?
Now, I cannot get a visa without a date that I will be departing the country (which I am not planning on entering).
That leaves me 2 options: find a very cheap flight back to the EU within a certain time frame + get a visa for that period or take the risk that they deny me boarding if I cannot convince them that I am not going to ALG (but what would be a good excuse for that?). Am I perhaps missing an option?