There's really no way to hide you're currently unemployed, or at least not employed in the tech field, unless you make up an entire fantasy world. Not only will you have to put the lie into your resume, and maybe provide fake references, but you'll also get tons of interview questions about skills and projects and challenges from your current job.
>"There's really no way to hide you're currently unemployed"
It is absolutely trivial.
>"but you'll also get tons of interview questions about skills and projects and challenges from your current job"
Your last job unless it is 10 years old should provide all of the answers. Any really identifying details should not be asked / answered as the employee is normally under NDA.
Same for references. Reference from "current job" can simply be refused. I can hardly imagine employee going to their boss and asking for a job reference while still working.
Anyways I am independent and run my own company. Maybe I am not up to date about how deep the US employers are able to stick their fingers up that proverbial hole.
While interviewing in the U.S. you'll get a lot of casual questions about your current job, such as what you like best about it, what skills you use there or why you want to leave. These will come from the recruiter, the manager and your future peers. These are both technical and social questions. Refusing to answer any of these questions would be very weird socially, and even very restrictive NDAs should allow you to at least speak generally about what you're doing.
>"While interviewing in the U.S. you'll get a lot of casual questions about your current job, such as what you like best about it, what skills you use there or why you want to leave. "
These fall perfectly into experience with last job. Does not have to be current. And all those questions you asked are trivial. Also I've never dealt with the recruiters. I have always searched and found perspective companies myself and no they were not Amazon big type. If I could not speak with the owner I would simply walk away - not my kind of place.
My first programming job in Canada - I just simply walked into the office and asked to speak to the owner (I knew it was small 20 person consultancy).
Since 2000 I am on my own but I still find clients and have interviews. Just a different type of interview of course.