The following is what happens to hit points and hit dice at the end of a long rest (PHB p. 186):
At the end of a long rest, a character regains all lost hit points. The character also regains spent Hit Dice, up to a number of dice equal to half of the character's total number of them.
Under this normal rule, the following two effects occur at the end of a long rest: the character regains all their hit points, and the character regains half their hit dice. These effects are independent (they manipulate different resources), so the order they occur does not matter.
The Slow Natural Healing variant (DMG p. 267) changes that rule in the following way:
Characters don't regain hit points at the end of a long rest. Instead, a character can spend Hit Dice to heal at the end of a long rest, just as with a short rest.
Under the variant, the following two effects occur at the end of a long rest: the character regains half their hit dice, and the character can spend their hit dice to recover hit points. These effects are dependent (they manipulate the same resource), so the order they occur does matter. Here's the problem: the order is not stated in the text. It's an emergent property of how those two rules interact with each other, and that interaction is ambiguous.
Disregarding the possibility that they happen simultaneously (which I believe is still ambiguous), there are two well-defined orders:
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The character regains half their hit dice, then they can spend their hit dice to recover hit points.
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The character can spend their hit dice to recover hit points, then they regain half their hit dice.
To show the practical difference, suppose I have 2 of 5 hit dice (each is a d8 with a +0 CON modifier) and I spend as many as I can. Here's the result under each case above.
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I regain 2 hit dice, leaving me with 4 of 5. Then I spend all 4 of them, leaving me with 0 of 5. I regained 4d8 hit points.
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I spend all 2 of my hit dice, leaving me with 0 of 5. Then I regain 2 of them, leaving me with 2 of 5. I regained 2d8 hit points.
Since the results are different, the order must matter.
Which is the correct order: regain hit dice first or spend hit dice first?
I do not think there is a RAW answer, so a correct answer will likely be RAI.
Best Answer
There's no difference.
But wait! In one case you regained 4d8, in another 2d8. Surely there's a difference!
But you're not really coming into the end-of-rest time in the same situation, despite the fact that in each case you've got 2 of 5 HD. You're comparing a character who exhausted all of their physical resources yesterday with one who didn't, and are finding that they today have different healing capacities. To see how this is the case, we need to backtrack a little bit, assuming that in either case the character had full HD a day ago1...
Case 1: regain, then spend--rewinding it.
In order to come to the end of the rest with 2 of 5 HD the character must have spent 3 HD at the end of their last long rest.
Case 2: spend, then regain--rewinding it.
In order to come to the end of the rest with 2 of 5 HD the character must have spent 5 HD at the end of their last long rest.
A day ago the character spent two fewer HD a day ago in case 1 than they did in case 2.
Case 1: regain, then spend--playing it forward.
You're correct that this character gets to now spend up to 4 HD.
Case 2: spend, then regain--playing it forward.
Your're correct that this character gets to now spend up to 2 HD.
Now the character can spend two more HD in case 1 than in case 2.
It may seem counterintuitive, especially given your correct analysis in the question-post. But there's functionally no difference in the two schemes2, it's just a bookkeeping thing3. That said, pick one as a table and go with it.
1 - if this seems disingenuous, know that all the following analysis relies on is the notion that there exists some time when the character had the same hit dice, and let's consider the day that follows that time.
2 - There might be an edge-effect at level-up, all depending on how you handle that as a table. But that also works out on the other end, so unless you're gaming your character down to the level of whether you expect the campaign to end on an odd or even level, it all comes to nothing.
3 - Only word in English with three doubled-letter pairs consecutive. Enjoy your daily dose of vitamin T.