I never advocate just dumping fresh wort into a filthy container and such humongous overpitching.
But, practically speaking, It Depends. If you're brewing a beer that should lack esters, you can get away with overpitching, so you can go ahead an knock out onto the old yeast. If you're brewing an English or Belgian beer, or any ale that's supposed to have an ester profile, harvest and pitch the right amount.
If you're going to pitch fresh wort the day of racking or within seven days or so of harvesting, you don't really need to wash the yeast. Just harvest the slurry into clean, sanitary Mason jars and keep 'em in the fridge. Then consult the Mr Malty calculator to see how much slurry you need to pitch.