I reckon you would be better off with a conventional type plastic insulated water bottle such as Camelbak Podium Chill

https://www.probikekit.com/cycling-a.../11232635.html (750ml)

https://www.probikekit.com/cycling-a.../11232624.html (610ml)

The stainless steel bottle as you mentioned doesn't fit your cage properly, and could also be slippery especially if you are hot and sweaty and risk getting dropped on the ground and going under your wheel (or someone elses) causing a crash.

The Podium Chill looks to be cheaper than the SS bottle too, though you will need to pay freight (if you look around you may find another place selling them offering cheaper/free freight)