If you measure RCBS 6.5X54 Mannlicher Schoenauer dies at the base they are about .005 smaller than the RCBS 6.5X53R dies. As a result you squash the base of your formed cases way undersize if they will yield. You are abusing your MS dies trying to size a solid .451-.452 dia case head to .446 to .448. The reason is the two rounds differ dimensionally. The 53R head is about .005 larger than the MS case. You will have sway back rounds that have to blow out each time they are fired.
If you do not have the right sizer, buy a Lee body or complete die for the 6.5 Carcano and polish the base open to about .453. Set it to locate the shoulder properly. RCBS and other MS seater dies are oversize enough to seat bullets in 6.5X53R ammo.

I sure would not use Swift brass due to the undersize case heads.

I use the more complicated sizing process because it will yield 100% good cases with no collapsed shoulders.

As far as thick necks go measure your chamber neck diameter.

Take a good 6.5X53R case and expand the neck with a long taper punch to about .310 to .315 diameter.
Then insert the case in the bolt face and shove it into the chamber. This will crush the funnel shape down with the chamber neck. Extract the case and measure it. It will probably measure .299-.300 diameter. If you do not believe you number just repeat the process. If you think you have a doughnut in your brass measure a loaded round can compare to the case neck diameter.