How do I get a lower natural regeneration rate?

Solution 1:

You could try turning off natrual regeneration, and using your own regeneration system of you own.
Of course, it's not perfect - But it somewhat mimics the pre-1.9 behaviors.

Step 1: Turn off Natural Regeneration

/gamerule naturalRegeneration false

Step 2: Create a clock that every four seconds runs the following command:

/effect @a 10 1 true
OR
/effect @a minecraft:regeneration 1 true

This gives a regeneration effect that's long enough to heal one health (half-a-heart) every four seconds, since heal heals by one when hunger is above 18 (9 steaks) every four seconds.

At Regeneration II, hearts heal at a rate of 0.8 hearts per second, therefore - 1 seconds is enough to give one health (half-a-heart), but not the second health to fill up a whole heart as a whole heart takes 1.25 seconds to generate at this potency.

Solution 2:

So you want your players to never starve, but also not to regenerate too quickly? Here's the best solution I could find:

First, we need to make sure the hunger bar stays at 19 so that both your players don't starve AND they regenerate slower. To do this, first, let's create an objective to detect the players' hunger.

1. Type: /scoreboard objectives add [YOUR OBJECTIVE NAME] food <--- This will detect the players' hunger levels. (whether they are on 20, 19, etc., but it'll NOT detect a certain hunger level
2. Put a command block and put this command into it: /effect give @a[scores={YOUR OBJECTIVE NAME=18}] minecraft:saturation 1 0 true <--- This will make it so that if a player's hunger is 18 and below, it'll put them back to 19.
3. Set the "Impulse" to "Repeat" and "Needs Redstone" to "Always Active" and boom! You're done! <--- This applies to the command block you just put on your server.

Remember, this only applies once your players' hunger effect starts to decrease, which won't be a problem since the hunger bar decreases quicker than the Speed II effect.

Now, if you did that all correctly, your players' hunger bars should stay at 19 and neither decrease OR increase. (unless you are planning to give them golden apples, then it'll increase)

And there you go! It's all done. Sorry for the late response by the way.