This is a case where you are definitely correct in theory, but in practice we can cheat and/or get screwed over. While it’s an angular momentum situation and no

This is a case where you are definitely correct in theory, but in practice we can cheat and/or get screwed over. While it’s an angular momentum situation and not linear momentum, one method of satellite attitude control is “reaction wheels”. Inside the SV, there’s a mass on a motor; to rotate the satellite about an axis, you spin the reaction wheel on that axis in the opposite direction (equal and opposite momentum). In theory, stopping the reaction wheel should result in the same outcome on the SV, but it doesn’t quite because some of the energy of the reaction wheel was burned off as friction heat. It’s a small effect that adds up over time. Even without this “speed it up to increase its mass” situation the OP is referring to, it seems to me that you could exploit something similar on a spacecraft for linear momentum, by allowing drag on, say, a tennis ball to be asymmetric by shooting it fast in one direction and slowly moving it back in the other. It’s not violating any laws of physics, just exploiting a second-order effect when the first-order effect isn’t going to get you anywhere. You’d eventually need to get rid of the heat, probably just by radiating it out into the void (and, naturally, it wouldn’t be an energy neutral situation, you’d need some kind of power source to make up for the losses)