Does this sound like a good idea?

Good morning,

I'm starting the cold plunge journey, but I'm on a budget and I live in an upstairs apartment... which eliminates most options like an legit cold plunge set-up outside or the chest freezer set-up. So my only option is to get some sort of 100 gallon tub into my bathtub, put ice in it while filling it with water, do my cold plunge, and then drain it afterwards... no big deal. But what's the best option to do that? I was thinking about getting a ice maker that holds 33lbs of ice, but the cheapest ice marker I found was $140, and I'll have to buy $30 adapter at home depot, and do some crazy installation to the water supply under my sink. So I'm thinking about buying [this] (https://www.amazon.com/gp/product/B0DNB8LMLH/ref=ox\_sc\_act\_title\_3?smid=A1AV1ITIV5DLPH&psc=1) & using these [large ice cubes] (https://www.amazon.com/gp/product/B0CYSM3J8C/ref=ox\_sc\_act\_title\_1?smid=A7O4VU3ZSZZBX&th=1).

Will my plan work? Will the ice cubes make the water 40 degrees cold?, or are ice cubes too big? How long would it make the 68 degree tap water to around 40 degrees? Would it be faster using a bunch of smaller size ice cubes, like 2lbs? I know it will require more work than a typical cold plunge set-up, but what other options do I have?

Thanks for your time.