There are a few values in GalCiv3GlobalDefs.XML that you can try tweaking:
- InfluenceRadiusRoot, which determines the nominal radius of the influence bubble around an influence generating object, with the nominal radius being (total influence generated)^(1 / InfluenceRadiusRoot). Making this value larger will reduce the size of influence bubbles.
- InfluenceMinToClaim affects rounding on the radius of the influence bubble, so it probably won't affect anything that you really care about.
- I don't know exactly what InfluenceBellCurveDivisor and InfluenceFalloff do, but I believe that they govern the 'shape' of the strength of your influence as it spreads out from an influence generator, as influence strength plotted against distance from the nearest generator more or less forms a bell curve around the generator (if two generators have overlapping bubbles, I think that the influence in the tiles where the bubbles overlap is determined by the sum of the influence from the two generators). At the very least, the InfluenceBellCurveDivisor should affect the sharpness of the bell curve (the width, however, appears to be set through the InfluenceRadiusRoot). You could play around with these and see if you can make them do something similar to what you want.
You could also find the places where the base influence generation rates are defined. There are, however, four entries that you'd probably want to change to do this - ImprovementDefs defines the base influence generation rate for colonies and the civilization capital (find the ColonyCapital and CivilizationCapital improvements, look for the entry for InfluencePerTurn), StarbaseModuleDefs defines the base influence generation rate for Culture Starbases (find the CultureRing module, look for the entry for InfluencePerTurn that has a TargetType of Starbase), and CultureTraitDefs defines the base rate of influence generation for starbases with the Benevolent tree perk that lets all starbases generate influence (ProminenceTrait4, look for InfluencePerTurn; note that this is additive with the value defined on the CultureRing). As most or all other influence modifiers are multipliers that act on these values, this is probably all you'd really need to modify, though you could, if you so desired, also reduce the magnitude of the various multipliers.
I think you could also go into GalCiv3AIDefs and give the difficulty levels you normally play against a bonus to influence generation, though I haven't looked to see if InfluencePerTurn is an allowed value for that XML file. Doing that would allow the computer's factions to better resist your influence, though you'd need to be careful not to overdo it.