The last thing I need is another coffee contraption. Would there be any difference between using a Toddy vs using a pitcher that I already own and then filtering it through a sieve lined with a kitchen towel? There doesn't appear to be anything special (physically) about the Toddy and I don't like the fact that the filters are proprietary.

There is indeed nothing particularly special about the Toddy. Its basically a plastic bucket with a filter and stopper in the bottom. The filters appear to be some kind of cloth. Its convenient that the bucket fits on top of the included pitcher, making it easier to do with one person (most other coldbrew methods require a helper).

I've also made cold brew in a stock pot, and poured through a fine mesh colander when done. The colander obviously doesn't filter everything, but it does better than you might think since the coffee itself acts as a filter. The remaining sediment settles to the bottom pretty quickly.

You can use jars for the infusion and strain through a fine mesh first then into a brew basket with a paper filter if you really want to take all the particles out. I did small amounts (2 oz of grounds and 8 oz of water) in jars and then poured them through Hario V60 pour overs, that seemed to work pretty well.

I haven't tried it yet but I though spreading the coffee out over a mesh like a splash guard for a frying pan would get more of the concentrate out of the grounds.

Heck, you can even just do it in a press pot