Spray foam in the exterior walls is an option and its pretty cheap. 

Maybe you can shave 1/2" to an 1" out of the wall so the actual tank is recessed into the wall.If recess a large enough area you can make it look like it was intentional.

You can trim that peg to make it fit, but guess what those "peg shavings" represent as applied to REI?

Does spray foam not work for the 4-plex?

One thing to consider... the exterior walls may not be insulated but this can be fixed with spray foam. 

Michael S. have all given great advice getting started.Here are a few more tips:Start here.

Well, seeing as you have knowledge in evolutionary biology, you've more than likely noticed that not all of BP is at the same stage...evolution-wise.Take my buddy @Brandon Turner - I keep telling him to shave that damn beard cause it makes him look like a stone-throwing Neanderthal.

I want to start renovating but afraid to show up, change locks, and then learn after the fact that the original owner(s) have been there on/off.

If it's in the process of being sold you need to contact a QI for info.  1031's have specific requirements and deadlines but are not tricky if they are followed.  

(Baffles are foam insulation sheets that create air tunnels behind the actual fiberglass insulation).