I think you have come up with a good way to handle the situation. It mirrors the rules laid out for vehicle to vehicle collisions, and it is straightforward.
As for material in the books, here are things I considered when this happened in my game:
What's in the rules?
There is nothing specifically in the rules about a vehicle running down a character. There are some elements which can help frame a rule or ruling, however.
Falling (p. 228 AoR)
The severity with which falls are treated can be used to guide the severity of a vehicle impact on a character. The falling distance could be mapped to the relative speed of the vehicle (Short to Speed 1-2, Medium to Speed 3-4, Long to Speed 5-6, and Extreme to Space speeds).
The Falling rule assigns an increasing amount of damage and strain to apply, as well as an increasingly dangerous critical injury. This could be a good fit for the basis of a ram attack with a vehicle, as it also offers a mechanic for the character to potentially reduce the damage (athletics or coordination check).
States of Health (p. 230, AoR)
Narratively, what will be the condition of the character after the hit? Beyond applying damage, strain, and a critical injury, there may be more to such a hit depending on the speed and type of interaction the ram caused. This rule offers good detail on how injury affects characters.
Relative Silhouettes Rule (p. 225 AoR)
How hard is it to hit the character with the vehicle in question? The Silhouette rule makes this easy to determine and easy to keep consistent.
Improvised Weapon Rule (p. 225, AoR)
This chart could help the GM to devise a sense of difference between ramming someone with a Swoop Bike at Speed 2 and doing so in a Repulsor Tank. Base damage could be determined by the piloting roll, modified by the size of the vehicle, and mitigated by the target's athletics/coordination check.
Vehicle Collisions (p. 256, sidebar, AoR)
Vehicles of sufficient size and/or shielding compared to what they hit might avoid damage from the collision. Guidelines as to when to apply it, how to try to avoid it, and when it can be ignored are offered in this rule.