I work with a lot of wool and what I would add is this: I would use a soap that does not need to be rinsed out (but you will rinse the quilt) such as Eucalan. Orvus paste is good too but this must be rinsed very well. I would fill the bathtub with cool water and dissolve the cleaning agent in the water and then place the quilt in the tub. I would gently press the quilt into the water making sure it absorbs the water. Use a very gentle scrunching motion and then let the quilt soak. You should see some dirt lifting into the water. I would then drain the water out (leave the quilt in the tub) and refill. Always make sure to use the same temperature of water, though, as Peckish has pointed out, the old fabrics have been worn and washed many times so I don't think felting is too much of an issue but I would still be careful. When you add more water just move the quilt aside. I would do this process until the water is clean.
Once it is clean and drained (still in the tub) I would gently roll it and squish it to get some of the water out. It will take some time because you should be gently. Do not lift the quilt. But you can roll and fold that roll up to squeeze the water out. Take a large towel or a couple of sheets and roll the quilt onto the towel to be supported and carried to where it should be layed out flat to dry. Once you are at that desitination I would have several dry towels available that I would keep putting the quilt onto and rolling them up in absorb the excess water. Finally, lay the quilt out for the final flat dry.
It is a lot of work to wash it this way but if you don't have access to a top loading machine or front loader with a soak and spin cycle then this is, in my opinion, the best way to do it. This is how I wash cashmere and handknit sweaters. This is also how I have cleaned heirloom textiles. I have also washed a king sized quilt with a wool blanket in the middle in this manner. It would help to have someone help you with manipulating it. I definitely would not send it to a dry cleaners and I would not use a laundromat unless you are very familiar with the machines and you have washed and cleaned the machine out first.