Spark Plug Tap Stuck in Head?

Hello all, I have a 5.4 triton in the truck listed above, Lariat. I had a spark plug blow out and tried using a tap without confirming socket size. I dropped it down There tapped it a couple times and realized I’m not going to be able to get that back out. My sockets are all too thick for the hole unless there is some insane thin socket set somewhere. I really don’t want to open this thing up. Anything helps thank you so much. This is after dropping an extension magnet all the way into the cylinder. That took a whole day. I also think I’m going to have to open her up because I can only assume there’s a lot of shavings inside. I’m lost y’all.