Forgive me if I get this wrong as I'm exceeding the limits of my physics knowledge here but what you're talking about sounds like what I would call a special re

Forgive me if I get this wrong as I'm exceeding the limits of my physics knowledge here but what you're talking about sounds like what I would call a special relativity model of thinking. The general relativity model is where everything has a constant spacetime velocity vector. So time dilation just expresses that higher velocity through space necessarily lowers time "velocity". So the special relativity view is to think of a straight line as the shortest distance between two points where the general relativity view is the longest proper time between two events in spacetime. So if we're just going to talk about velocity through space (rather than a constant spacetime velocity), it's best to think of velocity as a value with domain [0,c] rather than an unbounded real number because that's what we're used to dealing with.