Is this Tabaxi Monk/Barbarian/Rogue/Fighter movement speed calculation accurate?

Question

Dash is an action that can be taken by any character, and by some as a bonus action, and Tabaxi's racial feature feline agility can be used as part of their movement, not action or bonus action.

So a tabaxi's base speed is 30'. Assume my character is a 10th-level monk (+20' speed), a 6th-level Barbarian (+10' speed from fast movement), a 2nd-level Rogue (with the cunning action feature), a 2nd-level Fighter (with the action surge feature), and has the mobile feat (+10' speed). This allows a speed of 70'. a partner casts longstrider on me (+10' speed), so my speed is 80'.

The tabaxi feline agility feature is: "when you move on your turn during combat, you can double your speed until the end of the turn, cannot be used again until you move 0".

Assuming I need to run - while in combat:

1. Base speed 80'

2. feline agility "when you move on your turn during combat, double speed" now speed 160'

3. action drink potion of speed (gain an additional action, doubles movement)
   notice this does not double again, as an effect that already doubles my speed is in effect

4. haste action dash +160

5. action surge dash +160

6. bonus action dash (cunning action) +160

   = 640 feet

Now the next turn, I couldn't use feline agility, nor action surge, but would free up an Action, and the haste spell effect would double my speed.

1. Recalculating this, base movement 80

2. potion of speed in effect x2 (160)

3. haste action dash +160 (320)

4. action dash +160 (480)

5. bonus action dash (cunning action) +160 (640)

   = 640

As I understand it, if an effect would be repeated through use of item/magical means, they do not stack. In this case the "Doubles your movement" is the effect in question, as it is repeated through many means (spell, potions, racial abilities, and even boots) it only makes sense that it is not permitted to stack, but please, correct me if I am wrong.

Answer 1

Feline agility and the potion of speed both apply.

The rationale stated in the question for these effects not combining is:

an effect that already doubles my speed is in effect

However, the question assumes it is fine for multiple effects to increase speed by 10' (fast movement, mobility, and longstrider). The interaction between feline agility and haste is no different -- they are two different effects. Just as the three speed-increasing effects combine to add a total of 30' to the character's speed, the two speed-doubling effects when applied together quadruple their speed.

The rule about duplicate effects is specific to spells (PHB, p.205, emphasis mine):

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.

For example, if two clerics cast bless on the same target, that character gains the spell’s benefit only once; he or she doesn’t get to roll two bonus dice.

There's no reason to think that spells interact with other game features any differently. There are numerous examples of game features applying similar bonuses to game statistics; that's the way the game works.