using a chiller on your tank, base and/or column rather than Dry ice is pretty standard fare. generally done using jacketed (rather than sleeved as you have) parts.
you’re not going to get far with a DIY chiller -27C (no load) is the best I’ve managed. you want -50C or better.
do you TIG weld?
I have seen attempts at “jacketed” without welding, and I’d suggest you not take that route.
you might find some of the threads linked here helpful Dewar Ditty
and Search results for 'chiller hack' - Future4200 probably has good reading too