My Monarch is a little smaller, at 10,000 lbs.. When I move big machinery like this, I hire my local heavy truck tow company. Patrick, the owner, is used to rigging 75,000 lb. trucks that have flipped over and down in ditches, etc.......12K lb. machines are a piece of cake for him, and any other in that business, using his boom truck. With wood 4X4's attached to the sides of the bed to protect the lead and feed screws, he used lifting slings over head, and quickly found the balance point. He lifted the lathe off my trailer, nice and slow, and I drove out from underneath. He then used the boom to traverse out and under my shop door, and set the lathe down on 4X4's inside my shop. Took about 10 to 15 minutes. It's also how Monarch shows, in all their manuals, how to rig their lathes. You may want to consider a tow truck company with a boom truck. Patrick's is rated at 50 tons. I asked. He unloaded my Monarch and my K&T mill (6500 lbs.) for me for a few hundred bucks.
I have personally had some bad experiences with riggers in this area (Chicagoland), which I totally blame on myself for hiring the wrong guy. The ones that I have been forced to use, due to auction restrictions, seem to not give a shit how they treat things. These "things" they like to toss around and be rough with are our new vintage prized possessions, so I suggest checking out whoever you work with so that you are comfortable with them.
I'll share one more story......before using Patrick the first time, I hired a rigger for the same job (lathe and mill). He quoted me $500 over the phone. The morning he was supposed to show up, which I scheduled with him and took the day off my normal work schedule to accomplish, he called 30 minutes ahead of the scheduled arrival time and doubled his quoted price. I can only guess that he thought he had me over a barrel. I told him to pound sand. Be aware of that as well.