I can't speak to the quality of Shilen pre fit barrels but as far as the cartridge I have a few comments. Since you have a long action, there is no practical advantage to the 6.5 WSM over the 264 WM other than lack of a belt. You may encounter some feeding issues with the WSM and the factory mag box and follower, not sure on that.
If you do go with the 6.5 WSM I would go with the standard neck chamber as opposed to the .287 neck version. With the .287 neck chamber you are looking at having to turn the necks of the cases and getting a bushing die for sizing which runs into some time and money. You can get a set of Lee 6.5-300 WSM
dies for about $30-35 if you go with the standard neck.
The 6.5 WSM is pretty cool and duplicates the velocity of the 264 WM. Cases are easily formed from 270 WSM brass in one pass through the sizing die. It is a fun and easy wildcat if you decide to go that route. Just some food for thought.