The closest option for you is the Mission rod and gun club. They have a 300 yard range there and they also hold regular 300M drop-in shoots.
Kamloops has a 500 and soon-to-be 900M range.
You're right in that Vokes is a military range and one cannot drop-in to shoot there, but if you become a member of the BC Rifle Association, there are several organized shoots there during the summer.
You should think about coming out and jumping in with both feet and trying an F-Class match. In Kamloops and Mission, we have a sporter class that would allow you to shoot with the rifle you have, without having to invest in specialized equipment.
We actually have just such a match happening on the Halloween weekend in Kamloops. We would love to welcome you aboard and introduce you to several folks from your area that would love to help you along the way to long range shooting. Drop me an email if you are interesting in giving this a try.
regards,
Ian