An idea could be a decaying malus, dependent on the interactions of the two empires? More positive interactions decrease the malus over time, emulating your species getting over your differences?
Heck, expanding on that idea, it could be a variable malus, if you do something they don't like, it increases the negativity between your species. For instance, lets say you insult them. Alongside the insult malus, it could cause your ethos malus to increase as well, further lowering the total opinion. Essentially, this would cause empires of opposite ethos to suffer worse diplomatic penalties that are harder to overcome as opposed to those they have with empires that have less conflicting ethos.
edit for clarification: I think the problem is that there is little the player can do to overcome the ethos and policy maluses, nothing the player can do to alleviate the problems between the two empires.
Heck, expanding on that idea, it could be a variable malus, if you do something they don't like, it increases the negativity between your species. For instance, lets say you insult them. Alongside the insult malus, it could cause your ethos malus to increase as well, further lowering the total opinion. Essentially, this would cause empires of opposite ethos to suffer worse diplomatic penalties that are harder to overcome as opposed to those they have with empires that have less conflicting ethos.
edit for clarification: I think the problem is that there is little the player can do to overcome the ethos and policy maluses, nothing the player can do to alleviate the problems between the two empires.