I'm confused a bit but I think it is within my ability to address the first part of your proposal.
Velocity is relative, an object can have any arbitrary velocity depending on the reference frame you are viewing it in. Instead of viewing Newton's first law as saying that an objects velocity will not change unless you apply a force to it, think of it as saying that if you do not apply a force to it, it will not experience any acceleration.
I'm not so sure about the 'quantity of motion' stuff, but I'm fairly sure "Once you acquire momentum you acquire velocity" is a bad way of looking at it. Momentum is not an intrinsic property, it is simply mass x velocity, the only thing special about this particular mathematical combination is the value of it in a system does not change over time.
The flaw in the rod example is that you are treating the rod as a single object where the crucial part of the argument is that different parts of the rod act in different ways.
I'm not quire sure what you are getting at in the rest of your post, but I believe I found your inconsistency. It doesn't matter that acceleration changes, acceleration isn't conserved (I'm not even sure what that would mean), momentum is.