A 6 Creedmoor would be my answer. If you must have the expensive dies to reload, that changes things slightly on the cost analysis. RCBS 6 Creedmoor dies are only $50.
To really save money this is a great option
https://jaoutdoors.com/product/tikka-factory-barrels/
I'm using a 17 inch 1:8 twist Tikka 243 barrel at the moment. 20 inches is a touch longer than I would want with a can, but for that price I would live with it. A $30 dollar adapter from Precision Armament will get you to a standard thread size, a bottle of Rocksett is another $15.
VV lists N565 loads for 109 and 108 Bergers in 243.
Edited after I read that you have the tools to screw on a pre-fit. $200ish all in for a new threaded barrel is a steal and CO is dry enough I would not think twice about the chromoly.