Are you sure the head needs to be planed? This is a Cat after all, not a Chev. Straight edge it all directions.
Some shops will give you a long song about how they won't guarantee the work unless they can "do it right", which to them is everything you could possibly immagine in a machine shop. The final call is yours; be just a little skeptical this time.
There is a special puller for them and it drops down over the two studs that clamps the nozzle down in and the chamber has threads in it that the tool screws down in and then it is made to turn the top of the tool and it pulls the chamber out.Maybe if your Cat dealer has one he would lend it to you as I,m sure they would very seldom use it.
How early a 3J is it?
Late D3400 used a hex drive removal tool that could be duplicated by welding a couple of nuts on a bolt. Sorry. don't remember the size.π π
The early units needed a special tool for removal as seen in the attachment.