I wouldn't say there's a consensus because we can't say what will/won't happen in your particular case but I don't think any of us seasoned travelers think this is a problem. YMMV, of course.

As for your questions:

You'll check your bag when you check-in for your flight, the agent will tag your bag and off it'll go to screening. There is no need to declare the Rogaine at LAX. What'll happen when you get to your destination is another story; presumably you've done your homework on what's acceptable to bring with you into China.

It is commendable that you want to do this "the right way" and it sounds like you have. As for the "don't want any surprises" part, I would adjust that a bit and say to expect at least some mild surprises but hope for nothing too bad.

Good luck!