I'm not familiar with the Conquest. Does it have an A.O.? Sounds like a wicked case of parallax. If there is no A.O., what range is scope set to be Parallax free? Did you move your head about while sighting at 300 yards to ensure there was no parallax? There could be a problem with your scope. 300 yards isn't anywhere close to a stretch for your .300. I'm assuming you checked your mounts and they are rock solid. You are getting repeatbility at 100 and 200 yards. Did you lap your rings? Did you torque the fasteners equally and not too tight? This is where an inch pound torque wrench comes in handy.

I would suggest;
Try another scope, or at least do a close evaluation of your Conquest.
Borrow a chrono
Buy your Brother a set of dies for this caliber. WBY ammo is expensive.
Next rifle, work all of this out a month or 2 earlier, before your hunting trip.;-)