If you really want your chicks as healthy as possible get them out of that cooler. It's very difficult to get enough fresh air moving inside a solid structure and it is way too small for 6 chicks. If you are using a heat lamp as the heat source, it is also likely overheated.
Do you already have the coop and run built? If so, brood them outside in the coop using a brooder plate and they will be
much better off.
As for keeping the bedding dry and the water clean, make a baby bottle for them and suspend it from a chain so you can raise it as they grow.
View attachment 3533649
This was made from a $0.75 sports bottle I got from a thrift store and a vertical nipple that I got from the farm store in a pack of 4. You need a screw on lid with a flip top that you can leave open to prevent a vacuum from forming.
Chicks from hatch to 1 week should have 1 sq ft of brooder space. From 1 week to 5 weeks they should have 2 sq ft per chick. After that, you need to bump them up to 3 sq ft per chick or already have started the integration process into the adult flock where 3.5-4 sq ft minimum per bird is maintained at all population sizes.
Lots of threads have been started here discussing behavior issues with chicks kept in too small a space with nothing to do in the space. They need to have perches or other objects to jump up on, sunshine in some part of the brooder to sun bathe in, something to scratch around in etc. And lots of fresh air to prevent respiratory issues.
Given dry bedding with proper space per chick, weekly cleanouts suffice.