If you are still looking for an inexpensive way to a 6x45mm, I can suggest this. It is a Savage Axis with a Shilen Select Match SS prefit. I call it Frankenrifle Too (pictured below). The barrel is 22 inches, original factory contour, and has a 1 in 10 twist. You can build it yourself or have a gunsmith spin off the OEM barrel and put a new one on.
My first 6x45mm, Frankenrifle Won, is a HB beastie. It started life as a Stevens 200 (Savage Model 10 - pre Accutrigger) and was cobbled together with inexpensive bits and pieces I found on special. The barrel was the only expensive part at $300 USD.
The rifle below has a Boyd AT-One stock, aftermarket bolt handle and an RB trigger. You certainly don't need all of this. If you keep the original stock and use an Axis with an Accutrigger, you can pick up a prefit aftermarket barrel new for about $350 or less.
The target was the first five shots down the barrel after becoming a 6x45mm. The cartridges were made from military, once fired IVI brass, homemade 76 gr OTM bullets and 8208 powder.