A spatially varying Cochrane factor might be as viable as varying the exponent, with the data we have.
BTW, are we talking the speed the crew thinks the ship is moving at or the speed a distant observer thinks the speed is?
That's what I usually do. Made up a spreadsheet once where WF is basically C^(WF*ch) where Ch depends on the proximity to massive gravitating bodies (so warp 2 would be 1.3C in CIS-Lunar space, but goes up to around 20C in interstellar regions).
And specifically, for these purposes we'd be talking about the velocity of the ship relative to either its point of origin or its destination, either of which may also be in motion. For this reason, "warp factor" is really the only meaningful speed measurement since even traveling to a fixed point, actual velocity as a multiple of C can vary dramatically hour by hour, sometimes minute by minute.