Dave,
What a coincidence! I've recently switched to Berger for all my shooting too! That 300 is a MUCH better option for this type of hunting.
Actually, the Sierra MatchKings utilize a fairly thin jacket, substantially thinner than their hunting line (GameKings, Pro-Hunters). They don't recommend them for hunting apps because they're not designed with terminal performance in mind. In general, they behave much like FMJs and do not behave like hunting bullets should. Ask them, they'll tell you the same thing, and steer you towards the other lines I mentioned.
Berger, on the other hand, has put some serious effort into ensuring the sort of terminal performance that you're looking for. You didn't specifically mention the twist in your 300, but even the 210 only needs a 1x11" for stability. Im assuming that you meant that the gun has a short throat, as opposed to a tight chamber? Different issues entirely, but yes, your thoughts make perfect sense. A longer bullet seated into a short throat will necessarily intrude into the powder chamber, effectively reducing the capacity of the cartridge. As a general rule, I don't like having a bullet's BT and bearing surface too far into the combustion chamber. Sometimes unavoidable, but much like Barack Obama in the White House, nothing good can come of it. Give the 185 a go, and I'll bet you'll find it to be an excellent performer for you.
Hope this helps,
Kevin Thomas
Berger Bullets