I have a plain 20-250 with an 18" barrel. 3850 with 40 grain bibs. Would work with your bolt face. Barrel life does suffer. You could just run your .243 and go with 80 or 85 grain barnes bullets. I have used those plenty to save fur.
The 20-250 is the cartridge I'm going with.
I'm not trying to save fur, Just can't use any center fire cartridge larger than .20 cal in NY state restricted hunting zones.
I'm pushing the 40 Gr V max to 4,000 Fps in my 20 Practical with 4198 and if I can get near that with the 20-250 I'll be happy.
I'm looking at getting an 18" barrel too, as most of my shots are within 100 yards.
I shoot a 20 Practical also.
one product you may not be familiar with, but Hornady makes neck sizing dies, in both a short and long version...
I've got 4 or 5 of them, and got them from the factory IIRC, for about $20.00
I think they still make one in 20 caliber. It would be adjustable for multiple different calibers., as you are only sizing the neck. Long and Short versions are dependent on the length of the base caliber you are using...https://www.midwayusa.com/product/1011096636https://www.opticsplanet.com/hornady-neck-size-die.html
either 243 or 22.250, or even like 6 BR or 22 BR, it should be easy to neck any one of them down to 20 caliber.
If you use either one of the 22 cal cartridges, the 22.250 or the 22BR, a 22 caliber die in that cartridge, remove the spindle and then size down, which will also size the body down.. then use the neck sizing Hornady die to size down the neck, this way you are using the 22 caliber die as a body die.
For seating the 20 caliber bullet, a 22 caliber seating die works just fine...
For my 20 practical, this is how I load for it...223 die for body die, 20 cal Hornady Neck sizer to neck down the neck ( that is all I had to buy), and then use a 223 seating die to seat the bullet...
having the 223 dieset all I had to buy was the 20 caliber Hornady Neck sizer for $20.
If doing a 22.250 necked down to a 20.250 ( I have those die sets also, from several manufacturers), same thing... pull the spindle out of the full length sizing die, for the body, and then use the neck sizer from Hornady for the neck, and then the seating die for the 20 caliber bullet...
Been loading my 20 Practical this way for 10 plus years....
Good luck on your project..