I donít know the specific layout of your basement, but is there any place along the wall or whatever, where your drain pipe runs?
You mentioned jack-hammering the slab. Well, even if the final run for your sewer line is under the slab, somewhere there must be a soil pipe going up to the bathrooms in the main part of the house. You could move the washer there. As an FYI, check your machineís operating instructions. I was faced with a similar problem, and found our washer would pump vertically 5í. That might help.
As another option. They sell (along with the basement toilet system you mentioned) a basement pump for sinks and so on. That might work for your washer.