It is true that gluons are always moving faster than quarks, and it is true that the strong force is actively pulling quarks together, but that does not require protons to form. What follows is a lengthy explanation about how the important factor for being "bound" is total energy.

A proton is a bound state. A bound state is not possible with a high enough kinetic energy, because a bound state requires the total energy (kinetic and potential) to be <0. If the energy were 0, a system of two particles would have the same amount of energy as the case where the two particles are at infinite distance apart (0 potential energy) and at rest (0 kinetic energy).

Let's make an analogy with gravity. A fast enough planet passing by a star will not orbit the star. This is despite the force of gravity moving at the speed of light.

Let's make an analogy with atoms. A fast enough electron passing by a proton does not make an atom. This is despite the force of electromagnetic moving at the speed of light.

The fact that gluons move at the speed of light does not force quarks to be bound. So what determines if something is bound?

In the case of a planet orbiting a star, the planet has total negative energy due to its potential energy $-\frac{GMm}{r}$. For a circular orbit, the velocity will obey $\frac{v^{2}}{r} = \frac{GM}{r^{2}}$ so the kinetic energy is $\frac{1}{2}mv^{2} = \frac{1}{2}\frac{GMm}{r}$. So you can see the total energy (potential + kinetic) is negative. This is what defines a bound system, as you would need to put in energy for the planet to increase its distance from the star.

A similar analysis holds for an atom. Electrons have negative energy <=> they are bound to nuclei. Energy must be put in if you want to free the electron from the nucleus, ionizing the atom.

This is also why the Earth has an escape velocity. To become unbound from the Earth, a space traveller must have enough kinetic energy per mass.

It is true that gluons are always moving faster than quarks, and it is true that the strong force is actively pulling quarks together, but that does not require protons to form. What follows is a lengthy explanation about how the important factor for being "bound" is total energy.

A proton is a bound state. A bound state is not possible with a high enough kinetic energy, because a bound state requires the total energy (kinetic and potential) to be <0. If the energy were 0, a system of two particles would have the same amount of energy as the case where the two particles are at infinite distance apart (0 potential energy) and at rest (0 kinetic energy).

Let's make an analogy with gravity. A fast enough planet passing by a star will not orbit the star. This is despite the force of gravity moving at the speed of light.

Let's make an analogy with atoms. A fast enough electron passing by a proton does not make an atom. This is despite the force of electromagnetic moving at the speed of light.

The fact that gluons move at the speed of light does not force quarks to be bound. So what determines if something is bound?

In the case of a planet orbiting a star, the planet has total negative energy due to its potential energy $-\frac{GMm}{r}$. For a circular orbit, the velocity will obey $\frac{v^{2}}{r} = \frac{GM}{r^{2}}$ so the kinetic energy is $\frac{1}{2}mv^{2} = \frac{1}{2}\frac{GMm}{r}$. So you can see the total energy (potential + kinetic) is negative. This is what defines a bound system, as you would need to put in energy for the planet to increase its distance from the star.

A similar analysis holds for an atom. Electrons have negative energy <=> they are bound to nuclei. Energy must be put in if you want to free the electron from the nucleus, ionizing the atom.

This is also why the Earth has an escape velocity. To become unbound from the Earth, a space traveller must have enough kinetic energy per mass.

Edit: Aside from this confusion in your scenario #1, there is also the physics of asymptotic freedom, which you can read about here. In short, at closer distances, the strong force becomes weaker.