Stuffisgood, first and foremost, Welcome to the Brotherhood!!! You are in good company here, and info is always flying around on load data, and useful tips and experiences.
It sounds like to me you are well equipped in the gun and scope department, and reloading supplies as well. I was shooting the 168 Berger for a while, but have switched to the Barnes TTSX, TSX, and LRX. The H1000 is a great powder, and your primer selection is perfect. If the 1000 dosen't do the trick, try RL 25, and the same primer you are using. A few of us here have turned to the 25' and have had really good luck with it. It seems as though the speed is better, and more consistent, and pressures are lower.
Your load OAL is going to be in the 3.630 area, as the Winchester box is a little shorter than the the Remys, but believe me, it is no handicap. I to have a Winchester. Mine is a Custom Sharpshooter, and shoots like a dream. Mine will shoot 160 Grand Slams into a knot with 78.0 grains of 25, @ 3.630 all day long. But my load for that gun is 82.0- RL 25-140 partition, with a 215 GM primer. It shoots less than an inch at 200 yards.
You are going to fall in love with this bullet after you figure out what it wants to be fed. I have been shooting this round for about 16 years, and it still gives me goosebumps. But deer don't like it worth a ****!!!!
The Berger info is a good starting point, however it may be a little conservative. I'm thinking if you start around 78-79 grains, that will get you there, and watch for pressure signs, and of course your targets. A chrono is a huge help if you have one. If you don't, get one!! Otherwise you are shooting in the dark. Keep in touch. There are lots of good folks here to help you out a long the way. Nice score!!!!