Sometimes it's just easiest to take an existing game system and adapt it to what you need. That could certainly work with Ivory, where the planning stage can be mated with a different game system for the implementation stage. There are advantages and hazards to this this method. I'll discuss what, in my opinion, are the most important implications.
The largest hazard with choosing an existing RPG is that the system can distract the players. The system tells you what is important, and the players can easily end up designing a character that has no relationship with the logistical and exploratory part of Ivory. Alternately, because Ivory is so specialized, the needs of Ivory can distort the existing RPG into a mockery of itself as so many pieces of it go unused.
For example, if I were to implement Ivory with GURPS, it would warp GURPS. Since ST, DX, and HT matter little in Ivory, a winning character design would be to put all points into IN and into IN based skills. Someone may buy huge levels of wealth. The players will naturally expect to get benefits from these points that they've purchased, but there's little benefit to them as Ivory is about the players designing and solving their own problems, not about rolling dice to simulate solving those problems. Thus, strangely enough, GURPS would not work well at all despite its "universal" design.
Alternately, you could choose old style D&D, and because that game has so few rules, and isn't really malleable. Most of its rules don't actually intersect the Ivory parts of the game, which makes that simplistic and stiff system works better with Ivory. The players can't distort their characters into perfection. In addition, the lower-levels of that game are so randomly deadly that the players would still tend to avoid combat. This should come as no surprise to those who know that old game system because old style D&D worked similarly to an Ivory based system, where the players were left to their own devices to solve their logistical and exploration problems as they saw fit. There was no rolling dice to solve those problems. The early DM's relied upon the same principles as Ivory, which is that most problems were emergent and didn't need rules. You find this attitude demonstrated in the game's extensive price lists, worker pay list, and the informative chapters on building castles and kingdom building.
D&D 3.0/3.5/Pathfinder would work okay at best, but generally not be a good match for Ivory. This system puts the players into the wrong state of mind. Character development is significant. The cognitive overhead needed for understanding the system has become so large that players will have their attention pulled away. They will want their skills to apply. There are also too many opportunities to roll dice or cast spells to solve problems. That argues for a poor fit.
D&D 4 would be a poor choice. I quite like the game system, but the focus of the system is too far away from the focus of exploration and logistics. I rather suspect that D&D Next will share 4e's problem.
What other game systems might work? I don't know. I am, by no means, well versed in modern gaming. My best guess is that simpler game systems will work better than complex ones. In my guesstimation, what makes a good game system for Ivory is a lack of rules revolving around logistics and exploration, good price lists to base decisions upon, enough realism for the players to imagine the scenario, and low cognitive overhead.
Post 1: Ivory RPG