I don't think pursuing this change is productive at this point in development. The required influence relationship values for Federating will be based upon the desired game length. That is, if Arcen wants to make the game last 50 years on average, then these values will be changed to reflect the average growth of relationships over that period of time. However, the underlying mechanics of the race relationships are still needing to be modified, so any change and balance performed here, will need to be recalculated after the underlying mechanics are reshaped. Hence, spending time and effort on them now will be wasted, because everything will have to be redone again later.
If you really want to do it then, why not something simpler and more organic, just use the sum of the influence of each race in the Federation to the race looking to join. So if the Skylaxians are considering joining the Federation containing the Boarines (+100), the Peltians (+30), and the Burlusts (-230), then current Federation summed relationship to the Skylaxians would be -100 (100 + 30 - 230). You would then need 100 Influence with the Skylaxians to get them to consider joining the Federation. (the average of Federation race relations might also work).
This could also be done both ways, so Federation wide decisions could be made at some points, if the Federation has a -100 relationship with a race, they probably would want to tariff them, raid them, war with them, etc.
To get the other effect, just modify starting race relationships. For example the Skylaxians and Burlusts start at -200 relationship status. Or, better yet, just have the Burlusts and Skylaxians have a negative monthly relationship modifier. So if the Burlusts are being warlike (Blasted Burlust sum are just evil.) then Skylaxian relationships drop. And if the Burlusts are being neutral, they still drop (We can't trust those guys, everyone knows what they are like). But if the Burlusts are being really nice, then you can overcome then natural negative relationship trend and eventually get them to be friends (They control their violent natures, such a race would be a good friend).