Well, you're right that it's not a mathematical certainty that momentum is always conserved. But there's such a mountain of evidence for it that we should have

Well, you're right that it's not a mathematical certainty that momentum is always conserved. But there's such a mountain of evidence for it that we should have a very high bar for claims that it's violated. Thermal effects and measurement error are both likely sources of the discrepancy. But another reason to be skeptical is that Noether's Theorem tells us that a violation of conservation of momentum is only possible if the laws of physics are not translation invariant, and we should be able to use the violation of conservation of momentum to illustrate a specific instance where physical laws are not translation invariant. That would be Earth-shattering. (But not, strictly speaking, impossible)