Interesting suggestions - the problem with 'in-progress' culture scores is that they are pretty meaningless without other information. For example, a player could be really far ahead in culture and look like they are winning easily, but in reality have poor production, a weak army and not many actions - and just treading water before getting massively crushed in the later half of the game. Similarly, a player could have low culture on the score board and appear to be losing, but have epic levels of production making it clear that they will make up that ground easily in Age 3.
Although if the in-progress scores showed all information (similar to what the arrow button does in-game) that would be amazing.