I have switched from Rift to HP (Oculus to Steam) and was able to download a Steam copy of the game for free using a key provided by Frontier.
I originally purchased the game from the Frontier Store website, so not sure if purchasing though Oculus is different in some way.
Try this:
1) Go to the
Frontier Store website and log in using your Frontier credentials.
2) Click on the little people icon in the upper right. (2nd icon in from the right top, labeled "account dashboard")
3) on the left side menu of the next page, find "Partner Keys" and click on it.
4) You should see a listing of game keys for different platforms. (steam & oculus rift)
Hopefully you'll see keys for both Oculus and Steam.
IIRC correctly I had to request a steam key from the same website, I believe I did this by clicking on Elite in "My downloadable products" in the same menu as "Partner Keys", and requesting it. But I get an error today when clicking anything in the list, looks like a website problem.