Chris,
The thing I'd attempt to impress on you is that "matching" one profile to another profile isn't the way it works.
It's a fool's game to try.
The idea of profiling is basically to create a machine state -- the inking controls that are RIP specific -- and then to characterize the machine in that state; that characterization being the ICC profile.
And the end goal of the process is to be able to print the images you send the RIP correctly. Correctly meaning as close as you possibly can to match the L*a*b* values of the individual pixels in the digital file to the L*a*b* values in the printed image. And if you do that, then your printed images will match your originals as well as white point and gamut will allow.
So in this case, if the original file is what you sent the printer, I'd note first that it's not a particularly large-gamut image. The red and blue in the flag are the only two colors that should mute back just a bit, but otherwise, it should reproduce faithfully on your Mimaki.
And what I'd note of the two printed image samples is that each one just looks like a poorly made profile, not issues associated with any particular profile-making engine. Setting aside the obvious color issues, I'd note that both of them have some posterization going on in the flesh tones, and it appears all shadow detail in the jacket has been lost.
And that may very well be due to settings in the ICC profile build, but it's not due to the engine itself. Since the engine in Caldera and in i1 Profiler are the same, you could get these results from either engine.
And what I'd say, as gently as I can, is that it's also a fools game to try to get much better than this by looking for answers on the Internet. There is a ton of information out there online about color management and machine profiling out there -- and most of it is wrong. And you will waste an awful lot of time and money figuring that out.
If you're really serious, get professional help. It will save you money in the long run.
Mike Adams
Correct Color