In my bathtub there is a chrome plate with an overflow fitting on the bathtub upper wall above the drain area. My wife said that when the plumber snaked the drain he ran the snake through that fitting, not the drain in the bottom of the tub. However, I was not there to see him work and I'm not sure how difficult it was to use the overflow as a cleanout.

To keep the drain clean over time, the plumber told my wife to put a cup of household bleach in it every month to clean out the build-up. It seems to work to keep the drain flowing, and my wife believes it definitely keeps any unpleasant odor from building up.

Bruce

They do make skinny probes with hooks on the side which are theoretically supposed to clean out narrow drains. They may or may not do the trick.

You can get hair strainers which prevent the hairs from entering the drain. They come in several styles. I am not sure if any would work on your style but you can google the various possibilities. The most popular one is called "mushroom" something.

I found out the vinegar, baking soda, hot water alone didn't work. But when I plunged it after it quit bubbling it loosened up all the gunk and the drain flowed freely.

Try the Drain Millipede from the Container Store. I believe it is 3/16” in diameter. It works really well!