Can you grapple/shove with the Hunter Ranger's Whirlwind Attack?

Question

The Hunter Ranger's Whirlwind Attack feature states:

You can use your action to make a melee attack against any number of creatures within 5 feet of you, with a separate attack roll for each target.

The rules on "Grappling" state (the rules in shoving are effectively identical):

When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.

I couldn't find any other features spells or abilities that allow a creature to make a flat "melee attack". If they had said "melee weapon attack" instead this would have meant the same thing but specifically have excluded grapple/shove as an option.

I am unsure whether the rules on grappling/shoving mean that the only time you can grapple/shove are when you take the Attack action, which you are not doing when using the Whirlwind Attack feature.

I would like answers to assume that the following ruling made in the Sage Advice Compendium is correct:

Whirlwind Attack is unusual, in that it’s a single attack with multiple attack rolls...

Answer 1

No, you can't Grapple or Shove with Whirlwind Attack because of the wording.

Whirlwind Attack says you can use your action to make a melee attack, but that action is not the Attack action.

Grapple/Shove specifically says if you want to use it, you can use the Attack action to make a special melee attack.

As you're not taking the Attack action when you use Whirlwind Attack, the requirement for Grapple and Shove isn't met, so you would be unable to grapple or shove a creature targeted by it.

Thanks to @Medix2 for also pointing out that the Sage Advice Compendium says

Grappling and shoving are special melee attacks that require the Attack action (PH, 195).

Answer 2

It doesn't matter, because you replace the attack with grapple

Even if you could grapple instead of the Whirlwind Attack, you still grapple one creature, because grapple is not modified by your attack, it replaces the attack.

See the wording of the Whirlwind Attack feature, it still gives you one melee attack:

You can use your action to make a melee attack

The Grapple description says you can replace one melee attack with one grapple:

If you're able to make multiple attacks with the Attack action, this attack replaces one of them

So, you spend your action to perform the Whirlwind Attack ("a melee attack"), then you make a grapple ("a special melee attack") instead. This does not allow you to grapple any number of creatures, you still grapple a single one.

The same effect is achieved when you spend your Action to make a simple Attack action.