Phew...
Not something I would consider...
Is there a reason why you would not consider one of these pumps?
Not sure if it was the best solution but it was the most economical in my situation. When I bought my house, the previous owners had the washing machine discharging into the laundry tub which drained into the sump well. The sump pumped the water into the septic tank. This is against code where I live. Also, it made the sump well smell which was made worse every time I did a load of wash and churned up the contents of the sump.
I looked into the "box and pump" solutions but those required a vent, something that I did not have in the basement. Then I heard about these pumps by searching the web and figured it was exactly what I needed. Installed it 4 months ago and has been working well ever since. No smells either despite the lack of a trap.
Flotec also has a similar pump available at Home Depot (search for sink pump).
I would recommend that you also pick up a flood alarm that will let you know if the pump stops working and the laundry tub overflows.