Hello,
To my mind, albeit are paying rent/mortgage.. you are investing in your girlfriends property...
Say If you were just house mates / in a non romantic relationship would you still be willing to paying off your house mates mortgage? Probably not.. your name is not on the deeds..
To me, just agree a fair rent and pay that ( if you are unlucky enough to break up - it’s just rent) save what you can for a property (if you like) and invest together if that’s the way the relationship progresses.
My 2 cent!!