1. Ensure your chamber is clean. I know this sounds elementary but you would be surprised how little crud is needed to make a case hard to chamber.
2. Adjust your FL sizing die out several turns from its usual setting per the maker's instructions.
3. Put a lubed case in your press and size it. You will not contact the shoulder but don't worry just now. Wipe off the lube and chamber the sized case and check for resistance.
4. If resistance is felt turn down your die 1/2 turn and repeat 3. Continue to size, check and turn down the die until the case chambers to your satisfaction.. If you use up all your die adjustment then you may have to get yourself a small base die.
5. Trim your cases to length.

Unless you are getting neck splits or experiencing neck tension/bullet seating problems I would avoid annealing necks. Getting annealing right isn't as simple as some would suggest. Doing it wrong can be a waste of time to downright dangerous.