Sorry for late response.
My preferrence would be Transaction Plus.
With few additions:
First, we need to clarify whether it is desired to have experienced CMDRs impact the influence more than the beginners. If so, I would suggest to have the transactions modified by the CMDR's rank in the respective area. For instance, we might want to have Elite CMDRs having double the impact Harmless ones have.
Let me demonstrate on Trade (sorry for my ignorance, I don't know whoat impact the profit has on influence so i leave it out here). Also, for demonstration purposes, let's assume selling full cargo results in 1 INF point (it probably really does, doesn't it).
When you buy cargo, it is marked with the percentage of your cargo space it takes up (to prevent ship switching before selling).
I've got a Sidewinder with 4 tons of cargo space and my trading rank is Peddler.
I buy 2 tons of Gold. My cargo is marked being 50% influence worth.
I fly to my destination and sell with profit.
So, I have just added ,5 INF (because when buying my cargo was 1/2 of my cargo space). But my rank is a modifier, Peddler adding 33% (3rd rank out of 9). As a result, I've just added ,665 INF point to the faction controlling the station.
All other means can be modified in a similar way - exploring, bounty hunting.
Of course, it might be the rank modifiers are not what frontier would want, so then it's pure Transaction Plus for me.