That's a lot more work, parts, and cost than you really need to do.
I put a few scoops of, roughly, finished vermicompost in a bucket of water then mix it. I then pour that through a strainer / net / colander and use it within 10 minutes of first putting the compost in the water. The solids left over in the strainer go back into the worm bin.
The whole key is to keep the compost and microbes in it aerated and not going anaerobic.
Compost teas are usually a good weak fertilizer. One of the keys though is the live microbes in the tea. Sealing compost in a plastic bag or bottling the tea will kill the microbes. I would say you're far better making your own tea than buying it. Cost aside you don't know how long it has been sitting around without oxygenation. Old tea at best is liquid suspended compost and nutrients, at worst it is a stinky slimey mess.
Several people get very built up and complicated with making the tea - buckets, aerators, adding molasses and the like. The theory with this is you start to breed the good microbes in these brewers. Good microbes will displace bad microbes on the plant surface and in the soil and the symbiotic relationship between microbes and plant yield better plants... It's the concept of soil-food-web.
If you want to do a bunch of reading on this from someone that is well overboard with organic gardening try this link and surf through his site. I found this was good reading for the winter. While I don't wholesale subscribe to organic methods or shun the synthetics the organic guys do have some very useful ideas.
Growing up out on the dairy farm as a child, we would go out in the pastures with buckets and collect as much dry cow chips as possible. Bring it all back to an old cast bath tube in the back yard and fill it full. Plug the drain first, add water to it until it started breaking down. We would put a couple of bags of blood or bone meal in it for quick compost kick off and added a few dozen earth worms from our left over fishing bait boxes and it was on for a year. Let it set, covered with a piece of plywood. Once a month, I would dust the top of the bed with cornmeal and I had an everlasting supply of fishing worms and some of the most richest compost for tomato plants you could find. Transplant a few to that bed for a quick start root out and the volume of tomatoes those plants would produce was insane. Healthy, robust produce that were out of this world with flavor.