Also in this case I really don't mind disclosing - I was laid off because my position was made redundant entirely.
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.
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.
I think letting them know you are currently unemployed is a mistake. Frankly your current state of affairs is not their business. You can always tell them that you are ok but looking for a better job. Very simple and understandable. Yes it is a lie but it is the only reasonable option. Telling perspective employer to sod off and not to stick their nose into your internal situation is not going to do you any good. Telling that you are out of job and looking will immediately put you into unfavorable position. Treat yourself as a business in this particular case. Businesses have zero problems lying to each other / their employees for as long as it does not break a law.