You'll need to make very good joins betweeen the sheets of foil to make
that work.

Copper tape with conductive adhesive is ideal for this, but you had
better be sitting down when you look up the price.

Bringing a cable into an enclosure is the best way to bring in mobile
phone signals as well. When I needed to do almost exactly what you are
doing in a commercial test chamber I had to filter every signal
separately with feedthrough capacitors.

The chamber was quite impressive. They tested military vehicles in
there - even tanks - and could rotate them on a huge turntable.

John