From what I've witnessed in may other projects, switching from mod to standalone (usually to overcome the base game's limitation) is an idea that always come at some point in popular mods, yet rarely succeeds (and often means the end of the mod).
One of the most obvious example I know is the MagnaMundi mod for Europa Universalis 3: a huge mod that brought in a lot of new features, by far the most popular EU3 mod. The team came to the idea of developing it as a standalone to implement features that weren't moddable and to improve performance.
Paradox (EU's editor) had not so long before started to actively support developers willing to create games based on their own engines: they even provided (under NDA) the source code of their games to developers and I'm pretty sure they also provided funds/resources to projects. MagnaMundi was a perfect subject: there was already a team of motivated modders which had a good knowledge of the game and they had demonstrated they were able to deliver.
Yet, it was a failure. After several release postponements from the modders, Paradox (which followed the development closely) announced that they did not see the game being able to reach a stable state in the foreseeable future and the game was cancelled.
For other examples, another "standalone mod" under development called East vs. West based on Paradox' Heart of Irons 3 engine met a similar fate, though it was developed by a team which had successfully released a (less ambitious) standalone mod for HOI2. Although I can't say I follow very closely the development of this game, I've also heard that DayZ' standalone version was not going too well.
I don't know why this doesn't look to work out, but I'd guess it can be linked to the need for different skills than modding (project management comes to mind, not to mention much more advanced programming skills), underestimation of the time and efforts required to build the engine (how much time did it take for Firaxis to program CIV4?), demotivation from lack of "visible" results over a prolonged period, resources issues (it's not the same to help a mod and be able to leave anytime as to have to be sure you'll stay during the whole development), etc.
The worst thing is, as the most active people from a mod are leaving to develop the standalone, the mod stops being developed.
Bottom-line is, my advice: don't try to develop a dedicated engine for C2C, or I'd bet this would mean the end of C2C. There are surely limitations to the current engine, but resist the temptation to think that restarting from scratch will be worth the effort -
"Le mieux est l'ennemi du bien". There's still much one can do in C2C to further improve it without the need for a new engine - for instance, if speed issues are the main reason to go down this road, wouldn't the years it would take to do that be more efficiently used in just optimizing the current code?
