So if I understand correctly, under normal culture expansion, a city makes a claim on rings of tiles based on its culture level and then adds its current culture per turn to all tiles it claims, plus some bonus for tiles closer to the city tile than the outermost ring. Whichever civ has the most culture on a tile owns it on any given turn, assuming any civ has at least one point.
Under realistic culture expansion, rather than true distance < culture level +1 [which is rings and includes the 8 adjacent tiles at base culture=1], the determining factor in whether a tile is claimed at all is effective distance < culture level + 1, where effective distance is the true distance plus a factor for the terrain on that tile, plus a similar factor for each tile that culture has to go through to get to a tile in question. For tiles where this is true, culture is increased and control determined as in the normal manner.
Fixed borders does a number of things, but on a very basic level the difference is that, when active, on the turn a tile is claimed, the owner gets a sizable bonus which makes it harder for anyone else to exceed his culture total on the tile.
Maybe, if you wanted a similar effect to realistic spread, you could set some minimum culture required on a tile before it was claimed and reduce the culture added by some factor for effective distance (which I'm presuming is already calculated for the existing realistic spread effect). So a city would try to claim rings as under the normal system, but the actual culture assigned on a tile would be reduced by multiplying by something like
1/2^(max{0,Effective Distance-City Culture Level}l)
1/2 may be too big, perhaps 1/3? The max function is so this reduction doesn't become a bonus to tiles near the city.
I think this might be a fairly interesting system to watch, but at least one obvious downside is that claim of any new tiles would always be significantly delayed from the increase in a city's culture level, so that message would still have to be altered. Some kind of tooltip info for tiles a city is attempting to claim indicating progress would be necessary to have any chance of addressing DH's concern.
The threshold would have to be gamespeed dependant, but that's probably all as its terrain is already taken into account when determining the effective distance from the city. I don't know what a good value would be, and I only bring up the fixed border effect because some consideration of the relative size of the threshold and the fixed bonus would be necessary so one doesn't trivialize the other.
Anyway, just my $.02 at nigh 2 in the morning.