One option is to rush the FP in a second core by a leader. Just make sure you produce only veteran units, and try to have as many elite wins as possible. For this, do the easiest fights with your elite units to optimize their chances and lifetime.
Another option is as said to rush the palace with a leader after building the FP in your first core.
You can also do it without a leader however.
Build your FP in your first core, probably close to the palace.
Now build or conquer cities for a second core.
Grow the central city in your second core to be your largest city by adding workers to it.
Disband your capital and have the palace move to your largest city, being in your second core. The FP will now provide for the first core while your palace has moved to the second.
When you disband your capital, the game will decide the new capital city by city size and by the number of surrounding cities. It counts the cities in an 8 tile radius around the cities. (i believe it divides that count by 3 and adds it to the city size) The city that gets highest on this calculation will become the new palace. So if your second core has less cities in an 8 tile radius around the central one than the large cities in your first core, you might need to grow it a few extra citizens so that the size difference with other cities is enough to make up for the less surrounding cities.
Finally, you could use city ring placement.
All cities that are at the same distance around the capital will have an equal corruption rank. If you have say the closest 8 cities at the same distance, they will all have the low corruption like they are the single closest city to the capital. when counting distance to the capital, diagonal tiles are counted as 1.5.
When you get at a non integer number like 4.5, it is rounded down and it will be treated as 4.
There also is a bug that causes all cities that are close to the FP to get their rank not by cities that are closer to the FP, but cities that are closer to the palace.
This bug can be abused in 2 ways:
-Make sure your capital is remote from all your other cities, like on the other side of the map and have your FP somewhere in the middle of your empire. SImply make sure all your cities are closer to the FP than to the capital and all your cities will have no rank corruption. This abuse is illegal in gotm.
-Have a large ring around your capital, say distance 7 or 8, while having many cities around your FP at a distance closer than that. Now all the cities in the capital ring and all the cities closer to the FP will have no rank corruption. This abuse is not stated illegal, but it is one of the strongest and most abusive abuses you can use in civ3.
Note, none if this works in C3Conquests.