Yes, I agree. Closest to the body is the brain and that is also the part that's most important to the sound. "The sound starts in your head".
The mouthpiece is certainly what's next. I often change mouthpiece on tenor. A .500 bore sound very different with a small Bach 11C and a Hammond 12M (Bach 5-ish).
The leadpipe can change the horn a lot too. A cracked leadpipe destroys the sound of any trombone. The leadpipe makes the horn a player or not, that's pretty important. It can make the horn play big or small.
The slide and bell? I have not experimented with a lot of slides and bells on the same equipment so I can not confirm that but I know dents can be pretty big and still the instrument is not affected. It depends on where the dent is.
What I think; the equipment we choose make the sound we have in our head more or less easy to produce. If we have the possibility to change our mindset and imagine another sound we would NOT sound the same whatever equipment we are playing. When I change instruments I resign to what ever character the instrument has. I sound very different on my Yamaha 612R and my Holton 169 and my Bach 45 and my Conn 70h. I don't try to make them sound the same. The same goes for my tenors. If I want the same sound I would only use one instrument.