I have two Hoegger 12 quart plug lid milk totes. Love love love them. I have to transport milk in the truck in between barn and fridge, and the plug lid keeps the milk from going *everywhere*. Straight sided totes don't control leaks unless they are sealed.
I set the filter on top of the tote and filter each goat's milk as I go.
If you have a dedicated fridge, you can keep a large tub filled with water in it. Then, set the jars in the cold water and it chills it rapidly. If you have a large enough fridge you can set the whole tote in to chill.
I've also used the stainless pasteurizer pail as a tote and even cheese making vat. (grin)
One thing that might be difficult is cleaning. The totes are tall, so it's a pain unless you have a sink faucet tall enough for them to fit. Laundry sink may work.
Get one. They're expensive but I bet you won't be disappointed.
I got a plastic 'box' at a department store to carry all my milking supplies back and forth (and the egg basket, and a pair of work gloves, and...). I can easily fit four quart jars, the milk pail, and the egg basket. If I have eggs and more milk jars, I put the egg basket on top and can fit another two or three jars of milk. It's easy to wash out. You could go to the store and take a look at their laundry baskets and plastic storage containers, and see if one of them looks like it would work for you.
ETA: My box has handles and is about the size of most laundry baskets, although it's squared-off. It's lasted for a couple of years so far, so is pretty durable, considering the kind of use it gets! I can tuck one end on my hip and hold the other end with one hand to leave a hand free for opening doors and such. Tucking on my hip is only possible because of the squared-off shape -- a rounded-edge laundry basket would slide off. So that might be something to keep in mind, too.
Here are all but 2 of the does and the buck.
From top left Lovey, Mocha (both born this spring and just bred), Penny, bred for second time due in 5 wks, Glennis, 5th freshener, due in 5 wks, Lisle, second freshener, due in 8 wks, Inger, 1st freshener, due in 9 wks. Off camera are Marla, 1st freshener due in 9-10 wks, Meggie, 2nd freshener, due in 9-10 wks and Chip our baby daddy.
I believe in God's willingness to heal.
Cyngbaeld's Keep Heritage Farm, breeding a variety of historical birds and LaMancha goats. (It is pronounced King Bold.)