How well does the strong nuclear forces cancel out over large distances?

Photons, which don't undergo strong interaction, are still affected by gravitational field. This has been experimentally seen in e.g. gravitational lensing. This means that gravitational interaction, even if emergent, doesn't emerge from the strong interaction.

The strong nuclear force, i.e. the force holding the nuclei of atoms together,does not extend further than a fermi

The nuclear force (or nucleon–nucleon interaction or residual strong force) is a force that acts between the protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electromagnetic force. The nuclear force binds nucleons into atomic nuclei.

The standard model of particle physics fits the data very well with the forces described by the theory, and there is no mainstream physics possibility of of making gravitation an emergent force.

italics mine.

It is already a spill over force from the strong force between quarks, which grows stronger with distance, the force that binds the quarks inside the proton and neutron.

The strong nuclear force goes to zero exponentially fast beyond nuclear distances. It doesn’t need to be “cancelled” to go to zero, and it goes to zero far too fast to explain the inverse-square force of gravity.