Can the extra die from Orcish Fury be re-rolled with Great Weapon Fighting?

For things like Sneak Attack and Orcish Fury I know that they can be doubled on Crits per Crawford here.

We also know that only Weapon Damage dice can be rerolled with GWF. So, Sneak Attack or Smite would not get rerolled with GWF while standard weapon dice and the weapon’s critical dice can be re-rolled. For Orcish Fury it seems to me that it uses the appropriate phrasing for weapon dice similarly to the half Orc racial feature or Barbarian’s Brutal Critical and could thus be re-rolled with Great Weapon Fighting, no?

So, if we look at abilities like the Half-Orc racial feature which adds an extra weapon die on Crit and features like Barbarian’s Brutal Critical it seems to me that these could be rerolled with GWF since they use the phrasing of “adding another weapon dice” (normally Barb’s couldn’t get Great Weapon Fighting but now it’s possible via Tasha’s Cauldron of Everything and the Fighting Initiate feat).

For example:

You can roll one of the weapon’s damage dice one additional time and add it to the extra damage of the critical hit

from the Half Orc feature and:

you can roll one additional weapon damage die when determining the extra damage for a critical hit with a melee Attack

for Brutal Critical.

This phrasing seems very similar to the Orcish Fury phrasing which says:

When you hit with an attack made with a simple or martial weapon, you can roll one of the weapon’s damage dice an additional time and add it as extra damage of the weapon’s damage type.

My bet would be yes you can reroll the Orcish Fury Die with Great Weapon Fighting since it reads like we’re adding another weapon die and the phrasing is very similar to the half Orc feature. Have I got that right?