My problem: Take an old piece of paper / art / map. The paper typically has a yellow / orange tinge to it. Scan this into a Adobe RGB color space. Save as a TIF. Open in Photoshop - print to printer. The print has a magenta / pink tinge instead. The print looks the same if I use the correcr paper ICC or if I let the printer do the color management in Adobe RGB space.
I think you need to re-adjust your expectations with regard to what "out of the box" color can do for you.
Pre-canned profiles will typically be accurate to somewhere in the range of 2-10 delta E. Custom made profiles somewhere in the range 1-5 delta E. Typical workflows are all relative colorimetric based intents, where it is assumed that white is the white of the media (and it's wired up to make it that way), so the color inaccuracy manifests itself in areas other than white, and the above color accuracy is quite workable.
When using a proofing type workflow where you are trying to emulate one media color with another (Absolute Colorimetric intent), things get a whole lot more critical. I've seen many cases where 1 delta E is not enough - the media color error needs to be < 0.5 delta E to be a visual match. So "by the numbers" custom profiles may not quite enough, since the accuracy and repeatability of graphic arts instruments like the i1pro may not quite be good enough.
And then there are the other complications, such as the destination media simply being out of gamut of the source, FWA/OBE's in the paper resulting in color shifts because the instrument isn't "illuminating" the paper the same way you are viewing it. And then there is the scanner, which typically is not colorimetric (i.e. it doesn't see color the same way humans do), so profiling it with a test chart will not be accurate to better than 3-10 delta E, unless the test chart has exactly the same media and colorants as what you are scanning,
and the CIE reference values are made with the same illuminant as you will evaluate the result in. One of the errors you may well see with a profiling chart being different media to what you are scanning, is a white point error - by default (i.e. Relative Colorimetric) a perfectly profiled scan should result in the media color being removed. Typically people work around any such error by manually adjusting the white point of a scan to make the media perfect white.
[ And I won't complicate this explanation any more by going into observer variability. ]
Now all this doesn't mean that you can't solve your problem, or that it's not just one of these things that is causing the majority of the color shift (hopefully some of the preceding suggestions from people will help), but saying that "you spent a lot of money" so that it should "just work" isn't realistic, when you are using a less common workflow. A serious, high accuracy color instrument could set you back in the vicinity of $20,000 and up, so what constitutes "a lot of money" is relative.