Movement does not reduce your speed.
The way Speed works in D&D 5e is as follows:
Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round.
Some creatures and characters additionally have a flying speed, which is how far they can fly in 1 round.
After moving its speed on a turn, a creature ...
Movement isn’t Speed
Using your movement for a turn doesn't affect your actual speed. Even if you've moved 30, 60 (via the Dash action), or even 90 (double-Dash with something like the Rogue's Cunning Action) feet, your speed is still 30.
Your speed being reduced to zero is a result of things like being tied up or paralyzed, not just walking. Neither ...
Yes, Sentinel can stop Engulf
Sentinel stops a creature from moving when you hit it with an opportunity attack. Specifically, "its speed drops to 0" and "this stops any movement they may have been taking."
Engulf uses movement and speed. It says "the cube moves up to its speed." This is quite clearly movement. This provokes an ...
A tiny animated object with wheels has 80 feet of land speed.
The Corrupted Creature template can make it an aberation.
The Corpse Creature template can then turn it into an undead.
I'd love a simpler solution than this, if it's relatively on par.
The penalty is being in difficult terrain
You're in difficult terrain for all creatures occupying the same space:
The space of another creature, whether hostile or not, also counts as difficult terrain.
The constraint is that creatures in the situation must attempt to move out of it.
The rules have a provision that generally avoids the stacking situation:
Sentinel can stop Engulf, but not if the PC with Sentinel is the one being Engulfed (usually)
BBeast's answer is correct, but leaves out that a Cube using Engulf doesn't leave the target's reach, and therefore doesn't typically provoke an opportunity attack. However, the third benefit of Sentinel could let you stop it after it Engulfed someone else while in ...