I have big bottles of OTC stuff, plus a couple big bottles of prescription drugs that I get in maintenance quantities by mail order. No way I'm going to take them along in those huge bottles. I put them in those little pill strips for the length of the trip plus a few days, put elastic bands around them and throw them in my carryon. Been doing this for years and years and years for all kinds of international and domestic travel. I also carry a list of what I take in my wallet. Nobody's ever said a word. If they ever do, I'll show them the list. If they want to take the stuff to the chem lab, good luck to them.
Reasonable people can do reasonable things with reasonable impunity, even though in this case the letter of the law says you have to have the original containers.