Your position on quarks, that they are made-up constituents, was the mainstream view in physics from 1964, when Zweig and Gell-Mann independently proposed quarks, to November 1974, when the charm quark was discovered and everyone else decided it was the right idea. In this intermediate time, the idea of a permanently confined particle was considered suspect, so the theories of the strong interaction were not allowed to speak about hypothetical pointlike consituents. The quark model was still very strongly supported by indirect evidence, but in a sense it is good that strong interaction community rejected these ideas, otherwise we might never have string theory.
The phenomenon of confinement is not so mysterious, it was already understood on 1 dimension by Schwinger in the early 1960s. In 1 dimension of space, the electric force doesn't spread out as it does in 3 dimensions, and the force doesn't get weaker with distance. This means if you pull apart an electron and an anti-electron in 1d, at some point, you do enough work to make new electron anti-electron pair from the vacuum, and this pair-production neutralizes the two particles. This means that the only finite energy states are neutral composites. This was extended to the non-abelian case by 'tHooft, and the notion of confinement is completely understood in 1+1 dimensions.
The idea Gell-Mann indirectly promoted, and which was established by many people in the 1970s, is that something like this happens with quarks, that they are linked by a flux-string that makes the force constant, as if it were effectively 1 dimensional. This flux-tube idea was not well established in the 1970s, but you can't reject it anymore. Aside from lattice simulations, which show the flux tube in static-force calculations (the force between two quarks is constant with distance when they are far apart, just as in 1 dimension), there are also known exact dualities between string theories of infinitesimal flux lines and certain gauge theories that are similar enough to QCD that one can get a handle on how confinement qualitatively happens.
So the basic answer to your question is "no". It is as impossible for quarks to be wrong as it is for there to be no such thing as an antiproton. The evidence for quarks now comes from heavy-quark physics, where we can see spectroscopically the heavy quarks bound in non-relativistic bound-states with other heavy quarks. These charm-charm, bottom-bottom systems behave in just the way expected from nonrelativistic particles bound by a gauge force.
There is separate routine evidence from high-energy inclusive scattering. When you smash protons, you see jets, which are showers of particles in certain directions, and the jet emissions are correlated, so if you see three jets emerging, you can figure out the momentum of the objects which came from the collision point, and the probability distribution of the jet energy and angle can be calculated from QCD. The QCD calculations are in complete accord with experimental data, so much so that one has to go to high order of peturbations to match the distributions in complex multi TeV-energy scattering.