I think a hybrid format is the right way to do take-homes. The candidate is less likely to resent the time invested in the take-home if they have a chance to discuss or "show off" their work. It also gives candidates who have less free time to complete a polished solution the chance to say "if I had more time, I would [add tests, optimize this function, ...]>"

I still struggle with the "observer effect" during live extension exercises, but it's less pronounced than when starting with a problem from scratch. If I prepare a high quality solution in advance and do well in technical discussions, that's usually enough to offset any fumbling around during the live programming session due to interview jitters.