My vote would be to do Plan B. It will add value to the house and you'll want it if you ever decide to sell.
Washing machines pump the water out, and the pump in the washer will easily pump it up above the level of the washer. You could use the washing machine to pump the water up to a washer drain line and trap that drops down and is tied into the existing horizontal septic sewer line that is 3 feet off the ground.
I think that people use a separate gray water holding tank to avoid overwhelming the septic system with gray water, but I don't know for sure. And, there may be issues about making sure the laundry waste water is filtered so it doesn't clog the drain field from the septic tank. So, that would be something to research first.
If you are sure there is a drywell that the basement drain is connected to (and not just some type of French drain), then have a drain cleaning company come out and snake out the drain line and see how far the snake goes in before it reaches the drywell. That's a cheap first step before worrying about the Plan B of tying into the city sewer, or trying the other Plan B of tying the washer into the horizontal septic sewer line and possibly screwing up or overwhelming the existing septic system.