The FA large magnet isn't for removing the pins from the cases, it's for picking them up in bulk to move them.
My usual way is to tip most of the dirty water down the sink, then tip the remaining water, pins and cases into a 5L bucket.
Fill it with warm water (stops your hands freezing!) then pull out about 4 cases at a time, invert them so primer pockets are upwards over the bucket and shake to get any pins out, rinse in the water again to be sure.
Put those into another bucket or a large jug and repeat. Doesn't take long to do 100 cases, then rinse with clean water.
I then tip out the water in the jug, shake the cases and tip out the water again, I repeat this about 4 times to get most of the water out.
You can also run a telesopic magnetic pickup in the bottom of the jug to check for any odd pins.
After that I put about 50 cases into the middle of a medium towel, make it into a sling and spin it, centrifugal force gets more water out.
After all the cases are done I put them onto a pizza tray with some kitchen towel on it in a halogen oven on 80-100c for about 15 mins to dry.