Although formulas to calculate speeds from warp factors existed in the writer's guides, these were not always used consistently in the episodes and films. To explain the apparent discontinuity of the canonical warp factor speeds, background sources have given several explanations. Star Trek: The Next Generation Technical Manual
states the actual speed values of a warp factor are dependent upon interstellar conditions, for example gas density, electric and magnetic fields in different regions of the galaxy, and fluctuations of the subspace
domain. Also quantum drag forces and motive power oscillation cause energy penalties to a ship using warp drive. (pg.55) Star Trek Maps
introduced a similar concept as the Cochrane's factor, that influences the actual speed by multiplying it. It can be as high as a multiplication of 1500 to the relative speed within the curvature of space caused by the interstellar dust and gas of a galaxy, and as little as 1 in the empty intergalactic void. In the vicinity of massive objects it is so high that disproportionately high speeds are created, and they tend to result in the slingshot effect
. Between the galaxies there is only the empty void, so the speed follows only the basic cubic formula. (see below) Within the interstellar medium of Federation
space the average value for the Cochrane's factor has been calculated to be 1292.7238. (pg.6)
So you were right, the writers did try to explain some of the variations in calculations.