RCBS dies are rarely accurate. Take the stem out of the bullet seater and turn it upside down. Put a VLD bullet in the stem point down. I will bet that the stem makes contact on the point rather than the ogive of the bullet. The button on the size die is at the end of the decapping stem so it will have the least support and most wobble possible. So we will not use the button and avoid 25-06 brass with RCBS dies. The size die body without the stem might resize OK but if you check for concentricity with a runout tool I would bet on Redding or Forster dies being closer to true than RCBS. Besides RCBS dies are expensive!
I can come up with two plans for resizing 6.5-06 from 270 Win or 25-06 brass.
Redding makes bushing dies in 25-06 Ackley Improved. That die might work with 6.5 bushings. For example I use a .296 bushing in the 6.5-284. A titanium carbide drill bit might be necessary to open up the neck. It is a hardened die so this is not a walk in the park. Cost is $75.19 at Precision Reloading
Precision Reloading: 25-06 Remington Improved 40°
The second is CH4D has a 6.5-06 die set offered in 4 shoulder angles, listed for $82.
Caliber List : CH4D
Has anyone tried either of these or ideas or have an opinion?